Tagged Questions

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 ...

learn more… | top users | synonyms (1)

1
vote
0answers
4 views

Conceptual Question on Cramer rao lower bound for performance measure

In system identification, parameter estimation I have found in several papers that an analytical bound is derived which is the CRB of the error variance of the estimates. For, optimal performance of ...
0
votes
1answer
12 views

Probability from multiple trials

This questions is from a practice mid-term that I don't have a solution to. A monkey in a research lab is given 6 tiles with the letters AAABNN. On each trial the monkey randomly arranges the ...
1
vote
1answer
11 views

A hand of six cards is dealt from a standard poker deck. Find formula for p_(XYZ) (x,y,z).

A hand of six cards is dealt from a standard poker deck. Let X denote the number of aces, Y the number of kings, and Z the number of queens. a) write a formula for p_(XYZ) (x,y,z). b) Find ...
-3
votes
2answers
16 views

If 4 balls are drawn without replacement, what is the probability that at least 3 black balls are drawn? [on hold]

There are 9 black balls and 10 red balls in an urn. If 4 balls are drawn without replacement, what is the probability that at least 3 black balls are drawn?
0
votes
0answers
19 views

lottery game probability

In the "Make Money Game," the winning number is four digits, each selected at random from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, e.g. 0-3-9-6, 0-0-6-0, 9-4-7-9. A player may place any of the following types ...
0
votes
0answers
15 views

Lack of memory of a geometric distribution, proving a general case.

I have to prove this for a general value so $P(X > j+k | X>j) = P(X > k)$ Using the conditional probability I get that $P(X > j+k | X>j) = \dfrac{P(X > j+k) \wedge P(X > ...
2
votes
1answer
19 views

Frankie and Johnny game. What should Johnny strategy if he wants to minimize his expected loss?

Frankie and Johnny play the following game. Frankie selects a number at random from the interval $[a, b]$. Johnny, not knowing Frankie’s number, is to pick a second number from that same inverval and ...
0
votes
0answers
9 views

MTG: Probability of drawing a card with enough mana to play it (part 2)

This is a continuation of the original question: Let's assume we have the same scenario 12 White 13 Black 3 Spell Card 32 Other cards Based on the answers in Part 1, I can now answer that ...
3
votes
2answers
66 views

Probability brainteaser

I find this braintease on the internet and do not know how to solve it. For the second question, My first thought is to deduct from the situation when there is only 2 slots, then 3, 4, .., n,.. slots. ...
1
vote
1answer
17 views

What is the probability of success?

If I have 12 Possible questions, of which 5 are asked and I only need to answer 2 of them, what is the probability of my success (i.e., I am able to answer 2 of the 5 asked questions) if I learn 2 of ...
1
vote
1answer
23 views

Deck of Cards Probability Question - Probability of Getting At Least 2 Queens

There was actually another question like this but the final answer a person mentioned was incorrect and I was confused as to how he got it. Can any answers explain how they got there? I'd like to ...
2
votes
3answers
14 views

Symmetric Distribution of Random Variable

Prove: Let $X$ and $Y$ be random variables with the same distribution. If $X$ and $Y$ take only two values​​, then $X - Y$ are symmetrically distributed around zero. Note: 1 - You can use ...
2
votes
2answers
15 views

Probability of an event happening

Studying for a mid-term with a practice test, and there's no solution, so I want to make sure I have this right. A fire alarm has the property that it will ring with 99.5% probability, if there is ...
1
vote
1answer
10 views

Distribution of random variable $Y$ passed throught distributin function of $X$

If \begin{align*} F(x)=P[X \le x] \end{align*} is continuous in $x$, show that $Y=F(X)$ is measurable and that $Y$ has uniform distribution \begin{align*} P[Y \le y]=y, \, 0 \le y \le 1. ...
0
votes
1answer
19 views

Expected value of a sum of random events

Suppose there's a market that has decided to award its most loyal customers. The market sells a certain type of breakfast cereals with a single token in each box. There are n different types of ...
1
vote
3answers
15 views

Standard deviation…

I have this random variable $X = \{-1, 0, 1\}$ with uniform repartition $p(X = -1) = p(X = 0) = p(X = 1) = \frac{1}{3}$. Expected value is $$E[X] = \sum_{i\in\{-1,0,1\}} x_ip_i = 0$$ Then variance ...
0
votes
1answer
10 views

Determining the Likelihoods of Different Game States

Suppose a game is played in which Player 1 must gain two points to win and Player 2 must gain five points to win. Both players start with zero points. In any round, Player 1 has a $1/3$ chance of ...
0
votes
2answers
20 views

simple probability with marbles - requery

There is a post about how to calculate probability with marbles. I doubt the answer and i am asking for a more detailed explanation if possible. Picking marbles without replacement and without ...
0
votes
0answers
33 views

Probably, expected eatings on a roulette wheel

The probability that a roulette wheel stops on a red number is $\frac{18}{37}$ For each bet on “red” you are returned twice your bet (including your bet) if the wheel stops on a red number, and lose ...
0
votes
2answers
22 views

Conditional Probability - chance for an event to happen

I am learning probabilities at the moment and I have come across this problem: A person takes four tests in succession. The probability of his passing the first test is p, that of his passing each ...
0
votes
2answers
16 views

Probability CDF question on highest number of marbles pulled out

I'm kinda stuck on this problem. Here goes: An urn contains n marbles, numbered 1, 2, . . . , n. Suppose k < n marbles are drawn from it at random without replacement. Let X denote the highest ...
0
votes
1answer
39 views

Probability with expected value for diagnostic tests

Two percent of the population has a certain condition for which there are two diagnostic tests. Test A, which costs $1 per person, gives positive results for 80% of persons with the condition and ...
1
vote
2answers
30 views

A random variable $X$ uniformly distributed over the interval $[0, 2\pi]$

A random variable $X$ distributed over the interval $[0, 2\pi]$ a) the pdf of $X$ b) the cdf of $X$ c) $P(\frac{\pi}{6} \leq X \leq \frac{\pi}{2})$ d) $P(-\frac{\pi}{6} \leq X \leq \frac{\pi}{2})$ ...
1
vote
1answer
10 views

Probability: How to find what proportion is between the 2 values

Assume that head sizes (circumference) of new recruits in the Canadian armed forces can be approximated by a normal distribution with a mean of 22.8 inches and a standard deviation of 1.1 inches. ...
1
vote
1answer
18 views

Speed of convergence in probability

Let $X_i$ be a random variable. Let $\{X_i\}_{i=1}^{n}$ be a sample of observations i.i.d. over $i$ with $E(X_i)=\mu$. Let $\bar{X}_n:=\frac{1}{n}\sum_{i=1}^{n}X_i$. Let $\{A_n\}_{n \in ...
0
votes
1answer
16 views

What is the probability of at least 4 events occurring in 6 tries, given that $P(\text{occurring})=0.7$?

Problem: The plant is capable of growing seed 70% of the time. Calculate the probability that out of 6 tries, at least 4 seeds will be grown. A=seed is grown $$P(A)=0.7$$ From where do I start with ...
0
votes
2answers
13 views

Probability of defective of 1 item after picking 5 items out

I had a quiz and one of the question is : If I have 25 items among them 10 are defective. The question is I pick 5 out of 25 and test them, what is the chance of 3 of them are defective. The ...
0
votes
1answer
36 views

Probability - Diagnostic Tests, expected cost per person

Assume that for a randomly selected person: $P (D) = 0.02$, $P (R\mid D) = 1,$ $P (R\mid D') = 0.05$ So that the inexpensive test only gives false positive, and not false negative, results. ...
0
votes
2answers
18 views

Relations among notions of convergence

Let $\{A_n\}_{n \in \mathbb{N}}$ be a sequence of real numbers such that $\lim_{n \rightarrow \infty}A_n=0$. Does this imply that $plim_{n\rightarrow \infty}A_n=0$, where $plim$ is the probability ...
1
vote
2answers
37 views

Expected Value and Variance - Finding expected winnings

A game is played where a fair coin is tossed until the first tail occurs. The probability $x$ tosses will be needed is: $$f(x)=(0.5)^x;x=1,2,3,\ldots$$ You win $2^x$ dollars if $x$ tosses are ...
0
votes
1answer
18 views

What is the probability in the following case?

Given $100$ cells, each cell can contain the values $0$ or $1$ with $0$ - with a probability of $0.96$ $1$ - with a probability of $0.04$ How can I calculate the probability of having at least one ...
0
votes
0answers
18 views

Poisson Distribution word problems

During rush hour the number of cars passing through a particular intersection23 has a Poisson distribution with an average of 540 per hour. (a) Find the probability there are 11 cars in a 30 second ...
0
votes
1answer
25 views

Application of Slutsky's Theorem

Let $X_i$ be a random variable. Let $\{X_i\}_{i=1}^{n}$ be a sample of observations i.i.d. over $i$ with $ \mathbb{E}(X_i)=\mu$ and $Var(X_i)=\sigma^2>0$. Let ...
0
votes
0answers
17 views

Probability of accessibility

Between A, B, and C, there are the following highways: A – B, A – C, and B – C. During monsoon, when there is heavy rain, each of the road gets blocked independently with probability $p$. What is ...
1
vote
3answers
38 views

Find the pdf of T = X + Y

Let (X,Y) be a random point chosen uniformly on region R = {(x,y) : |x| + |y| <= 1}. I need to find the pdf of T = X + Y. I know the joint density is just equal to 1/(area) = fxy(x,y) = 1/2 for ...
0
votes
1answer
30 views

Probability: What ist the expected value of the number of comparisons made during a linear search?

I would like to propose the following problem: A linear search is performed to check whether a given name 'N' is on a list. The list contains 10 distinct names. The details: The search begins by ...
0
votes
1answer
12 views

Mean of a sampling distribution.

Suppose $\hat{p}=1/\overline{X}$ is an estimator of the parameter $p$ of a population variable $X\sim\text{Geo}(p)$. Suppose $p=0.36$ and $n=25$. What is the mean of the sampling distribution? This ...
2
votes
1answer
24 views

Proof of equivalence of two inequalities in Probability

Can you please give me a hint how to prove, that $P(A|B)>P(A)$ and $P(A|B)>P(A|\neg B)$ are equivalent? Thank you I think i have to add, that $0\neq P(B)\neq 1$ and $0\neq P(A)\neq 1$.
2
votes
0answers
26 views

Hitting line dartboard?

Assume that a beginner hits a dartboard. What is the probability that you exactly hit the border line between 13 and 6? We were thinking that the probability is zero because the probability of ...
2
votes
3answers
47 views

Probability of $2$ boys in a family.

In a family there are 3 children with minimum $1$ boy.What is the probability there are exactly $2$ boys in the family? I think I have to use combinatorics to solve this problem. I have solved some ...
2
votes
1answer
37 views

Probability conundrum

Good morning, wondered if you could help me please? I would like to work out the probability of and event happening 5 times out of 6. all 6 events have a 1 in 60 chance of a particular outcome. I ...
1
vote
0answers
34 views

Probability Distribution for a Weird Card Game

I promise this is not for a homework problem, even though this sounds like only something a professor would dream up. Here is the game: I begin with a deck of 13 cards: 1 through 10, Jack, Queen, and ...
0
votes
1answer
34 views

Probability - Airplane overselling tickets

Few days ago, I came across a question for probability in one of the interview. Question : The same small commuter plane has 30 seats. The probability that any particular passenger will not ...
2
votes
1answer
18 views

compare $cov(aX, bY)=ab \;cov(X, Y) $to $Var(abX)$ using the marginal distribution $f_X(x)$

I am trying to compare the proof $cov(aX, bY)=ab \;cov(X, Y)$ (which I have already found) to $Var(abX)$ using the marginal distribution $f_X(x)$. I am not sure where to start.
0
votes
1answer
21 views

Distributing work among cupboards

I am self studying, and have the answer to this question at the back of the book. The question is as follows (paraphrase): A survey of chemical research workers has shown on average that each man ...
1
vote
1answer
16 views

Bivariate Continuous Distributions

What is the marginal density of $X$ and $Y$ given the probability density function, ${f(x,y)= \lbrace3x ,\;\;0\le y\le x\le1}$
0
votes
1answer
39 views

Exam grades and bell curve

What is the mathematical explanation for the tendency of exam grades to conform to a bell curve? Initially, I was thinking it should be explained via the central limit theorem, but it's not clear to ...
1
vote
0answers
22 views

Gaussian random vector with 0 mean [duplicate]

Let $X =(X_1,X_2,X_3,X_4)$ be a Gaussian Random Vector with $\mathsf E(X_1)=\mathsf E(X_2)=\mathsf E(X_3)=\mathsf E(X_4)=0$. Show that $$ \mathsf E(X_1 X_2 X_3 X_4) = \mathsf ...
1
vote
1answer
20 views

Poison distribution variance,probability. and mean.

Let $X$ be the poisson random variable such that $P(X = 2) = 9P(X=4) + 90P(X=6)$ a) find the mean and variance of $X$. b) find P(X $\geq 1$) c) find P(X $\leq 10$) Ok so for the first question I ...
2
votes
1answer
12 views

How is this Variance found in this old question?

On this question: Probability: Normal Distribution they find these values: $\hat\mu = .05(150) = 7.5\space,\hat\sigma = \sqrt{150(.05)(.95)} = 2.67$ I see how they got $\mu$, but how did they get ...