This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under ...

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185 views

A fair dice is tossed 6 times. What is the probability that there is at least one pair of identical consecutive face values?

For example, 231146 is a valid sample point but 131213 is not. This is a question on past exam that i have no idea to solve. Please help me!
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3answers
143 views

It rains half the time in London…conditional probability

It rains half the time in London and the weather forecast is correct in its prediction 2/3 of the time. You live in London and you always take an umbrella if the forecast predicts rain, and you never ...
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1answer
46 views

probability question of paper class 11

In a box there are 2 red, 3 black and 4 white balls.Out of these three are drawn together.The probability of these being of same colour is what a. 1/84 b.1/21 c.5/84 d.3/21 well i'm bit confused ...
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1answer
46 views

Probability of NOT getting a straight or flush

What is the probability of NOT getting a straight or a flush in a 5 card poker game ? I tried this i) Count all the straights and eliminate the straight flushes from it. This will give the number of ...
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1answer
67 views

Expected value of two independent binomial variables

Find E[(X-Y)^2], where X and Y are two independent binomial random variables with n = 3, p = 0.4. I simply rewrote it as E[ X^2 - 2XY + Y^2 ], but can you assume that E[X^2] = E[X] x E[X]? If so, as ...
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1answer
93 views

Probability Question: Round table meeting

Six delegations have a round table meeting. The meeting organization randomly arranges the seat for them. It is important to consider who is sitting to the left or right for each delegation. How many ...
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1answer
31 views

Counting cases?

I don't have a background on probabilities but i do want to get the rule to solve the following problem and similar ones . Let's say we have a 2x2 matrix , in which every element could be either 1 or ...
2
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1answer
91 views

Spinner game outcomes: What has the best chance of winning with your last two coins?

We are discussing probability and odds in my elementary math class. The students came up with two scenarios. They are as follows... In a spinner wheel game based on the days of the week, students bet ...
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1answer
72 views

probability, normal distribution mean [closed]

Should I use a certain table for this question or should I use a special formula. A random value has a normal distribution with the mean 102.9 and the standard deviation 4.7. What are the ...
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0answers
42 views

Central Limit Theorem with no mean given

Samples are to be taken from a random variable $X$ which is normally distributed with standard deviation equal to $5$. Find the size of the sample needed so that the sample mean is within $1$ unit of ...
0
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1answer
37 views

Math homework guidance - mean probability distribution

95% of people must queue at a shopping line in a supermarket for 30 seconds before being able to continue. What is the distribution mean of the number of people among 20 randomly selected people who ...
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2answers
397 views

Poisson process and uniform random variable

Question: A single-pump petrol station is running low on petrol. The total volume of petrol remaining for sale is $100$ litres. Suppose cars arrive to the station according to a Poisson ...
0
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1answer
33 views

Is extra sum of squares $SSR(X_p|X_1,…X_{p-1})$ in multiple regression always positive?

An extra sum of squares $SSR(X_p|X_1,...X_{p-1})$, assuming that no pair of predictor variables are perfectly correlated, measures the marginal reduction in the error sum of squares. Eventually one ...
2
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1answer
65 views

Probability of n events out of N that choose the same object

I have to calculate the probability of n people out of N that choose the exact same object, among ...
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6answers
260 views

Probability that there are exactly two wrongly addressed envelopes

There are four Envelopes with letters. Two are chosen Randomly and opened and found that they are wrongly addressed. Find the Probability that there are exactly two wrongly addressed envelopes. My ...
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2answers
130 views

Combinatorics question - seats

In how many options can we arrange random number of men (identical men) in line of 15 chairs but: 1. 2 men can't sit next to each other. 2. next to each empty chair - there is at least one men. i ...
1
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1answer
58 views

12 balls in a box to distribute by 2 bags.

There is a box with 12 balls inside, 4 green, 5 blue and 3 black. We want to take out 4 balls for each one of 2 bags (bag A and bag B), and we take note of the number of balls of each color that the ...
1
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1answer
38 views

Show that Px$(B(s)\ge0 $ for all 0 $\le s \le t$ and B(t) $\in$ M) = Px(B(t) \in M)$-$P-x$(B(t) \in M)$,where B(s) is brownian motion,x>0.

I want to show Px$(B(s)\ge0 $ for all 0 $\le s \le t$ and B(t) $\in$ M) = Px(B(t) \in M)$-$P-x$(B(t) \in M)$ where,x>0,M is measurable set in [0,$\infty$). The difficulty for me is how to handle ...
0
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1answer
31 views

Determining hypothesis test and application

I'm running into issues trying to figure out what type of test to use and whether two tailed or one tailed in different scenarios. How do you determine what to do in the scenarios presented? For ...
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0answers
45 views

Exponential distrbution problem.

Let $\tau$ and $\sigma$ be independent exponentially distributed random variables with rates $\lambda$ and $\mu$ respectively. Let $S=\tau+\sigma$ and $m=min(\tau,\sigma)$. We need to compute ...
4
votes
1answer
105 views

How to find $\mathbb{E}[X\mid\min(X,Y)]$?

Say I have two independent variables $X$ and $Y$ that are exponentially distributed with respective rates $\lambda_X$ and $\lambda_Y$. How do I compute $\mathbb{E}[X\mid \min\{X,Y\}]$?
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3answers
423 views
2
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1answer
195 views

Testing hypothesis using significance levels

A random sample of n=26 observations on escape time (sec) for oil workers in a test resulted in sample mean 370.69 and sample standard deviation 24.36. Suppose the investigators had believed a priori ...
2
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1answer
14 views

Calculate $\mathbf{E} \left( \sum_{k=1}^{\infty}\xi_k \langle e_k,h\rangle \right) \left( \sum_{j=1}^{\infty}\xi_j \langle e_j,g\rangle \right) $

Assume that $H$ is a separable Hilbert space and $\{e_k\}$ is an orthonormal and complete basis of $H$. $\{\xi_k\}$ is a sequence of normal Gaussian random variables that are independent. We know ...
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1answer
43 views

Elementary Malliavin Derivative question about definition.

I am reading a book that defines the Malliavin derivative $D_tF$ as follows: If $F = \sum_{n=0}^{\infty} I_n(f_n)$ is the Wiener Chaos expansion. $F$ is in the brownian filtration and $F \in ...
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0answers
17 views

Probability of subsequences of sequences of Bernoulli random variables [duplicate]

I have a sequence of iid Bernoulli random variables $X_1, X_2, \dots, X_n$ with $Pr(X_j) = p$, and I'd like to know (a lower bound on) the probability that there exists a consecutive subsequence of ...
0
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1answer
48 views

What properties does dollar cost averaging have?

For example, say I have a bet with positive expected value. Say my money can become 2.1 times or lost with probability of 50%. There is a technique that specify how much money I can bet to say ...
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2answers
124 views

Calculating probability of pressing button three times and hearing sound at the third press

Consider the situation: There are two mysterious buttons in front of you. One of the buttons is harmless, whenever you press it, nothing happens. The other button is mostly harmless, when you press ...
0
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1answer
35 views

Limit in probability of $(\bar X)^2$

Hello can some one point me in the right direction with this question? Let $ F(x) = \begin{cases} 1- x^{-4} & x>1 \\ 0 & elsewhere \\ \end{cases} $ be the CDF of a random ...
2
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1answer
74 views

Generating functions and the blue eyed daughters

There is a famous problem, given that a man has a number of daughters and if you were to meet two of them at random there is a 50% chance that both have blue eyes. How many daughters does the man ...
1
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1answer
53 views

Probability, Uniform Distribution.

Suppose $A$ is a random number chosen uniformly from the interval $(-5,6)$,what is the probability that the quadratic equation $x^2 + Ax + 1 = 0$, has no real root? This is my approach, Using the ...
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3answers
624 views

Prove the lecturer is a liar…

I was given this puzzle: At the end of the seminar, the lecturer waited outside to greet the attendees. The first three seen leaving were all women. The lecturer noted " assuming the attendees are ...
0
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1answer
41 views

Central Limit Theorem help needed

Good evening. I have tried to solve this problem with many approaches but I have not succeeded yet. A man wants to estimate the mean number of water in meters cubed in a village. Sample used is $45$ ...
0
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1answer
84 views

When tossing a coin, what's the likelihood of coming up heads when it came up 999 tails consecutively? [duplicate]

Consider that you're tossing a coin $1000$ times. First $999$ times, it came up heads. Is it $50\%$ chance that the coin tails after $1000^{th}$ trial? Are these discrete events? Since the mean of ...
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0answers
35 views

Probabilities of throws of Archimedian solids

For the Platonic solids (and for e.g. the 10-sided dice), each face has trivially equal probability of showing up on a random throw. What could one say about throwing the Archimedian solids from math ...
0
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2answers
105 views

Combinatorics and probability: size of sample space

I'm having a tough time finding the next example's sample space's size: We have at our disposal the following: the three letters $\;a,b,c\;$ , and the five digits $\;1,2,3,4,5\;$ . We have to form ...
1
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1answer
31 views

The square-integrability of $\sum_{k=1}^{\infty}\xi_k \langle e_k,h\rangle,\ h\in H$

Assume that $H$ is a separable Hilbert space and $\{e_k\}$ is an orthonormal and complete basis of $H$. $\{\xi_k\}$ is a sequence of normal Gaussian random variables that are independent. It seems ...
2
votes
2answers
54 views

Convergence of the probability of a R.V.

I'm trying to solve a certain problem but I'm stuck at a point. The problem is: I have a uniform r.v. $U$ on [$-\pi,+\pi$] and I have a sequence of r.vs $X_1,X_2...$ where $X_k=cos(kU)$. Then I have ...
3
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1answer
172 views

A linear growth model with immigration

Ill give some background first before asking questions.(the text below is straight out of the book) Each individual in the population is assumed give birth at an exponential rate of $\lambda$ in ...
2
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0answers
51 views

PMF of a specific run in $n$ Bernoulli trials

What is the PMF of a specific run of length $k$ in $n$ Bernoulli trials with $P(X_i=1)=p$? Say, what is the PMF of the string 010011 (here $k=6$) in $n$ trials ($n>k$)? This question was initiated ...
1
vote
1answer
65 views

Conditional probability of random variables

Say I have random variables ~$Exp$ and lets call them $X$ with rate $\lambda$ and $Y$ with rate $\mu$. How do I find $\mathbb{P}\{X>Y|Y>4\}$? I know that $\mathbb{P}\{X>Y\} = \frac{\mu}{\mu + ...
2
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1answer
2k views

Word and Latex: Probability

I was practicing my probability and counting solving ability when I came across this rather interesting question on the web: The Reviews editor for a certain scientific journal decides ...
0
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1answer
87 views

probability of both balls of same color

Boxes 1 and 2 contain 4 white, 3 red and 3 blue balls; and 5 white, 4 red and 3 blue balls respectively. If one ball is drawn at random from each box, what is the probability that both the balls are ...
2
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0answers
45 views

Expected value of winning with a Random Uniform Variable

I have this small homework I don't quite understand. The problem is formulated as a game. (Who wants to be millionaire) You start with 1£. money = 1.0£ You can choose to quit at anytime So you can ...
7
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2answers
658 views

Why does probability change as you change perspective?

I was trying to solve the following question: Out of 2 Boys and 2 Girls, two students are chosen to advance to the next level. What is the probability that two girls advance to the next level ...
0
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1answer
30 views

Probability density function of a random variable

How to find a Probability Density/Mass Function for a random variable without assuming it follows a predetermined distribution, say, Normal or Poisson etc,. Lets say i have two hours of data of ...
2
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2answers
53 views

Marginal PDF integral not converging

If I have the following marginal PDF of independent random varibales: $p_X(x)=1 , 0<x<1$ $p_Y(y)=\frac{1}{2} , -1<y<1$ To get the joint PDF of: W = XY Z = X I can use the following: ...
2
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2answers
696 views

Free Throw Probability and Expected Number of Points

Suppose a basketball player has an 80% chance of making a free throw. The player was fouled and now has two free throws. If a free throw is made it counts as one point. Let X be the number of points ...
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2answers
49 views

Using continuity correction for normal distribution

Suppose a fair coin is tossed $900$ times. Find the probability of getting more than $475$ heads. Use the continuity correction. My answer: $n=900, p=1/2, q=1/2$ $\mu=900(1/2)=450, ...