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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3
votes
2answers
65 views

Which is the impossible voting in election?

Three candidates A, B, C are contesting an election. In an opinion poll fraction $a$ of voters prefer A to B, fraction $b$ prefer B to C and fraction $c$ prefer C to A. then which of the following ...
2
votes
1answer
313 views

Finding new probability density function with change of variable Y=sqrt(X)

Say we have a given distribution, such as X~No(a, b). I am trying to find the pdf and mean for $Y=\sqrt{X}$. I know the steps for finding the PDF, but since Y can only take on positive values, then ...
0
votes
2answers
1k views

Exponential distribution moment generating function to find the mean

With mean = 2 with exponential distribution Calculate $ E(200 + 5Y^2 + 4Y^3) = 432 $ $E(200) = 200 $ $E(5Y^2) = 5E(Y^2) = 5(8) = 40 $ $E(4Y^3) = 4E(Y^3) = 4(48) = 192 $ $E(Y^2) = V(Y) + ...
2
votes
2answers
99 views

A basic doubt on joint distribution

How to calculate the following probability $P(X \leq x, Y=y)$ where $X$ is a continuous random variable and $Y$ is a discrete random variable. I have been given the distribution of $X$ and ...
0
votes
1answer
41 views

$2$ Problems on probability

I've $2$ problems that I've encountered while solving some old exam papers. Problem $1$ On a table there are 3 fair coins lying. $2$ coins are facing head up and $1$ is facing tail up. You have to ...
0
votes
1answer
153 views

Expected length of generating a pattern (throwing dice)

A fair die is tossed repeatedly. The experiment ends as soon as the last six outcomes form the pattern 131131 What is the expected length (i.e. the number of rolls of the die) of this experiment?
0
votes
1answer
137 views

Probability question with false negative and false positive

A disease occurs in 1 out of 100,000 people. A person with this disease has a 99% probability tested positive for the disease, and a person without this disease has a 0.1% probability tested positive ...
0
votes
0answers
41 views

Question about $t$-distribution

The random variable $T$ has a $t$-distribution with $20$ degrees of freedom. Find the value of $t$ such that (a) $P(|T|>t)=0.98$ (b) $P(|T|>t)=0.05$ For part (b) am able to find ...
0
votes
1answer
232 views

Calculating the Probability of N people attending the wedding.

I have a list of N invitees to whom I have sent the invitation. I know the individual probabilities of each invitee attending the wedding. I would like to calculate the number of invitees who are ...
0
votes
1answer
334 views

Combining random variables

On combining random variables and their means, this article states: Suppose you have two variables: $X$ with a mean of $μ_{x}$ and $Y$ with a mean of $μ_{y}$. The mean of the sum of these ...
2
votes
0answers
180 views

Stationary Distribution of Doubly Stochastic Markov Chain

For a doubly stochastic markov process defined by a n by n transition matrix, does the stationary distribution go to p = 1/n for each state? If so, why?
4
votes
1answer
321 views

Background for studying and understanding Stochastic differential equations

Assume I have back ground of the following knowledge based on the textbook as : ODE : ODE by Tenenbaum Baby probability : Ross 's baby probability Baby real anlysis : Bartle's introduction to real ...
0
votes
1answer
133 views

Bag of Marbles Probability

My problem states: A bag of marbles has the following 21 black, 23 yellow, 21 pink, 27 blue, 24 green, and 19 orange. Reaching into the bag you grab FIVE marbles. What is the probability all 5 are ...
1
vote
1answer
44 views

Prove $\lim_{n\to \infty} P(n^{1/2} \cdot (\bar{x} - 1 ) < t) = P(Z < t) $ ($X$ exponential)

$x_{i}$, $i = 1, 2, 3, \dots$ i.i.d. from exponential ($\lambda = 1$) $Z$-standard normal r.v. $$ \lim_{n\to \infty} P(n^{1/2} \cdot (\bar{x} - 1 ) < t) = P(Z < t) $$ It seems like I could ...
0
votes
2answers
347 views

expectation values and square roots

If I have an expectation value $\langle{A^{2}}\rangle$ = $\langle{B^{2}}\rangle$, is it possible to take the square root of both sides, and say that $\langle{A}\rangle$ = $\langle{B}\rangle$ ?
4
votes
1answer
671 views

Great Monty Hall application in real life?

Suppose you are doing a multiple choice question with 4 different answers you have no ideas about. You mentally choose one (say A), and as you are about to write that down... you suddenly remember 2 ...
0
votes
2answers
1k views

a part of expected value of Poisson distribution $E(X^2)=λ^2+λ$ proof?

a part of expected value of Poisson distribution : $E(X^2)=λ^2+λ$ What is the proof? (except using the Moment-generating function )
3
votes
1answer
157 views

If $X$ is independent of $Z$ and $Y$ is dependent with $Z$ is it possible for $X + Y$ to be independent of $Z$?

Suppose $X, Y$ and $Z$ are three non-degenerate random variables. Suppose that $X$ and $Z$ are independent and that $Y$ and $Z$ are not independent. Is it possible for $X + Y$ to be independent of ...
0
votes
1answer
35 views

Does this inequality hold for a Lipschitzian strictly decreasing function?

There is a function $f : [0;1]^n\rightarrow \mathbb{R}$ which is Lipschitzian and strictly decreasing in all variables. Is it possible to prove either one of these two statements? There is an $M > ...
1
vote
0answers
21 views

How can I find the probability of a value occuring in an interval of a given step function?

Knowing a step function $N(t)$ defined over the interval $[0,T]$, which takes values in $0, 1, ..., k$, how can I define the probability $p(n)$ for $0 \leq n \leq k$, which is the probability of a ...
0
votes
1answer
105 views

calculating mean squared error for the Mean.

Exam Question There are two independent random variables $X_{1}$ $\&$ $X_{2}$ that are having normal distribution with mean $\mu$. Further Var$(X_{1})=1$ and Var$(X_{2})=2$.an unbiased estimator ...
1
vote
1answer
120 views

Combinatorics / nCr - How do I set this up?

A Bag contains 5 red and 5 green gumballs. If you select 4 of them without looking, how many ways can you get exactly 3 red or exactly 2 green gumballs? I am unsure of how to start his. I know it has ...
0
votes
0answers
34 views

Properties of convergence in distribution?

If you have a random variable, W which converges in distribution to N, and another random variable X which converges in distribution to B: i) Will W multiplied by X converge in distribution to N ...
-1
votes
2answers
70 views

How do I solve for $Ex(Y)$?

Suppose a plant has $X$ offspring in a year with $P(X = x) = \frac14$ for $X = 1, 2, 3, 4$ and, independently, each offspring has from one to four offspring in the next year with the same discrete ...
0
votes
1answer
41 views

Finding the probability

The random variable $T$ has a t-distribution with $10$ degrees of freedom. Determine the value of $t$ for which $P(|T|>t)=0.1$. My computation by considering $2-2P(T<t)=0.1$ , I get $t=1.812$ ...
1
vote
1answer
52 views

Real Analysis Estimate of a Lebesgue measurable function

I am trying to prepare for a qualifying exam and I came across the following question. I'm not sure how to proceed. Could you please give me a hint on where to start? Let $\{f_n\}$ be a sequence of ...
1
vote
1answer
84 views

Probability exercise with apples

We have a tree with 100 apples. There are 10 red apples and the rest are green. Lisa is picking apples at random. When she pick the 3rd red apple she stop. What is the probability that Lisa has ...
1
vote
1answer
52 views

Likelihood Function for Censored Model

I have a model that results in the following data generating process: $$x=\begin{cases}\begin{array}{c}y-\theta\\0\end{array} & \begin{array}{c}if\ y>\bar{y}(\lambda_1)\\if\ ...
3
votes
1answer
736 views

Rolling standard deviations

I am trying to calculate standard deviations on an array of numbers. My psuedo code looks like this: ...
3
votes
1answer
431 views

The Exponential decay.

I am studying semiconductor physics. there is a paragraph about Drude model in E.spenke's book "Electronic semiconductors" page 259 in art §9: "if on the average, a time $τ$ elapses between two ...
0
votes
1answer
28 views

question in probability

We have a test of 10 question. Suppose we have a student that answer 8 correct answers. What is the probability that he answer 4 correct answers of the first 5 questions? There isnt connection between ...
1
vote
1answer
31 views

A basic doubt on Poisson

For a Poisson process the event "arrival at time $t$" = ${N(t+h)-N(t) =1}$ when $h->0$. Is this correct ? How ?
2
votes
1answer
73 views

Outcome probabilities for set number of dice rolls with conditional extra rolls

If we are allowed $n$ rolls of a dice, where each roll of 1 gives us an extra roll, what is the probability of rolling m 1s in the sequence of available rolls, and likewise what is the probability of ...
2
votes
2answers
65 views

Probability with two random variables

Suppose two basketball players throw alternately to a basket (infinity times). Player A has probability of 0.7 to score, player B has probability of 0.4 to score. Player A is starting. What is the ...
0
votes
1answer
339 views

Probability of a node being connected to another

I am a newbie tinkering around with graph theory. Please pardon me for asking something very basic. Let us say I have a graph with n number of nodes. I have a binary adjacency matrix that specifies ...
1
vote
1answer
88 views

time sampling of a Poisson process

In Sheldon Ross, one paragraph has a heading "time sampling of a Poission process" and it describes that each arrival we toss a biased coin with $p(t)$ being bias prob.Then the process generated is a ...
1
vote
0answers
80 views

A graduate probability problem

Consider a real-valued random variable $X$ with $E[X^4]=1$. We know that $E[X^3]\leq 1$. If also $E[X]\leq 0$, find an constant $c<1$ such that $E[X^3] \leq c$ and find the smallest constant $c$ ...
0
votes
2answers
813 views

Joint density function of X and X+Y, standard normal random variables

Let $X$ and $Y$ be independent standard normal random variables. Find the joint density function of $X$ and $X+Y$. My attempt: $P(X=x \cap X+Y=z)=P(X=x \cap X=z-Y)=P(X=x \cap Y=z-x)=$ ? As you can ...
1
vote
1answer
114 views

Probability - Testing for diseases

I am just learning probability in my Discrete Structures class and am very lost. This is the example given in the book and I have no idea how to solve this problem. Problem: Suppose one in 1000 ...
1
vote
1answer
37 views

Joint distribution of RVs involving rolls of die

We roll a die until we get $4$ fives. Let $X$ be the number of rolls needed for the first $5$ and let $Y$ be the number of rolls needed to get the fourth five. What is the joint probability mass ...
1
vote
1answer
312 views

Convolution of indicator functions is continuous

Suppose I have an indicator function on a set of measure $E$, which is a subset of $[0,1]$. Is the function of this indicator convoluted with itself a continuous function? How can I show that it is? ...
4
votes
0answers
134 views

Card game probability

Suppose the following solitaire with a standard deck. I turn four cards visible on the board and on each turn, I remove those suits that appears more than once in the board. Then I fill the board such ...
0
votes
2answers
174 views

Probability of 2 points uniformly distributed over unit square

If either point is above or on the y=1/4 line, or below or on the y=-1/4 line, then the two points are definitely on the same side of the x-axis. For the other possible points I know I need to ...
3
votes
1answer
374 views

Unknown number of colours Bernoulli Urn

Okay, so, in the traditional Bernoulli Urn problem, we have an urn with a number N, possibly infinite, of coloured balls, and there are k possible colours. That one I grok. However, what if I don't ...
2
votes
1answer
44 views

Easy probability ..

I want to make sure these answers are correct A class has 10 freshmen, 8 sophomores, and 12 seniors. On a recent test, 3 freshmen, 5 sophomores and 3 seniors got an A. a) What is the probability ...
0
votes
1answer
2k views

How many flips to get at least one heads and at least one tails?

A coin having probability $p$ of coming up heads is continually flipped until both heads and tails have appeared. Find the expected number of flips. Here's my guess: $$E[\text{at least one head and ...
1
vote
3answers
145 views

Urn Probability (need multiple ways)

I need multiple ways to solve this question. Thank you! There are $A$ black balls, and $B$ white balls in an urn. You select balls one by one from this urn randomly without replacement. What is the ...
0
votes
1answer
240 views

Conditional probability involving a geometric random variable

Let $X_1 , . . .$ be independent random variables with the common distribution function $F$, and suppose they are independent of $N$, a geometric random variable with parameter $p$. Let $M = ...
0
votes
1answer
96 views

Drawing uniformly, and sampling with replacement for blue balls and without replacement for red balls

Take a bunch of red and blue balls, and place them in an urn. Let $r$ be the number of red balls, and $b$ be the number of blue balls. If we sample balls uniformly, and if they are red, discard them ...
0
votes
2answers
55 views

Mapping Normal distribution to a new bounded distribution.

My question is vague. I am looking for distributions that can be obtained from Normal distribution by mapping it to a bounded interval. "By mapping" I mean that a probability distribution ...