3
votes
2answers
35 views

Binomial dependent on a Poisson

I have been working on a problem with a binomial rv dependent on a poisson rv and have worked through to this point: $P(X=x) = \sum_{n=x}^{\infty} \dfrac{n!}{x!(n-x)!} p^x(1−p)^{n−x} ...
-2
votes
0answers
33 views

Birthday Problem [on hold]

This is an extension of birthday problem, please help In a class of 85 students, let X be the number of students who share a birthday with at least two other members of the class. a) ...
-1
votes
2answers
26 views

Geometric distribution related probability questions [on hold]

I am learning Probability, and I have this problem. Suppose $X\sim {\cal Geom}(p_1)$ on $\{1,2,3,...\}$, $Y\sim {\cal Geom}(p_2)$ on $\{1,2,3,...\}$, and $X, Y$ are independent. Let $S=X+Y$. ...
0
votes
1answer
61 views

Probability and coin tosses

Taking a Probability & Statistics class this term and trying to get my head wrapped around how I calculate coin tosses with specific out comes in mind. We're using the nCr and nPr functions on our ...
-2
votes
1answer
32 views

Baye's theorem may be required. [closed]

A message is sent which consists of $n$ binary symbols $0$ and $1$. Each symbol is distorted with a small probability $p$ (is changed to the opposite). To be on the safe side the message is repeated ...
-1
votes
3answers
68 views

The chance to double 1000 points into 2000 points [closed]

You own 1000 points. Your goal is to reach 2000 points, the only way you gain points is by gambling. You will always gamble 40 points, your chance of winning a 40 points gamble is 60%, how high is ...
0
votes
5answers
63 views

Bicycles: probability question?

I know this is quite easy but I would appreciate the help. In a survey, children were asked if they owned a bicycle. The results collected were: $46$ more pupils said ‘No’ than said ‘Yes’. ...
0
votes
1answer
29 views

Board Game Markov Process - Transient Probabilities

I need to write an essay on the Game of Life board game, and so I studied up on Markov Chains to help me calculate the probabilities and average payoffs for the spaces; however I'm not sure whether ...
1
vote
1answer
24 views

Proper formula for this probability

I have here a probability problem that I was able to solve without using any proper formula, i just made it up myself. I wanted to know the proper formula approach for this problem: Amanda has ...
1
vote
2answers
43 views

Not sure with my probability understanding

I have here a problem that I am trying to solve but I am stuck somewhere and I am not sure if i am doing it right or not. Erin has some coins in her pockets. In her left pocket she has 1 nickel ...
0
votes
1answer
45 views

Need explanation about probability

I wanted to learn about probability, I have here a sample question that i want to base as my starting point. This was given as our homework but was never discussed in class on how to solve it. ...
0
votes
1answer
30 views

Mantel-Haenszel $\chi_1^2$ statistic

I was doing a particular example from the book Epidemiologic Research by Kleinbaum(example 15.6) and didn't understood some basic statistical aspect. ...
1
vote
1answer
56 views

The pdf of $X+Y$

$X,Y$ are independent. $X\sim U(0,1)$ and $$f_Y(y)=\cases{2y,\;0<y<1\\ 0,\;Else.}$$ What is the pdf of $X+Y$? (i.e. $f_{X+Y}$) I know that $$f_X(x)=\cases{1,\;0<x<1\\ 0,\;Else.}$$ But ...
0
votes
1answer
35 views

Question about exp. distribution

We know that $X\sim \exp(1),Y\sim \exp(2)$ and they are independent. What is $P(Y>X)$? exp=Exponential... Thank you!
2
votes
3answers
158 views

We throwing $m$ balls to $n$ cells…

We throwing $m$ balls to $n$ cells randomly... At each cell can be more then one ball, or (of course) it can still empty. What is the expectation of the empty cells? I'd like to get any help! Thank ...
0
votes
2answers
282 views

Two groups A and B are playing a game…

Two groups A and B are playing a game. The first group that wins 3 times is the winner. The probability that group A will win at on game is $\frac12$ and the same thing for group B. $X$ = The number ...
-1
votes
2answers
29 views

We are making a Bernoulli experiment…

We are making series of independent Bernoulli experiment with $\frac13$ chance to success. What is the probability that we got success at the first experiment, if we know that we get two successes at ...
0
votes
3answers
278 views

What is the probability that A will win…

Two players are rolling two dices, if they get 6 Player A wins, if they get 7, player B wins, else they rolling the two dices again... What is the probability that A will win? I'd like to get any ...
1
vote
1answer
17 views

probability and random sample

suppose that a body mass index for a population of 30-60 year old men follows a normal distribution with mean 26 and standard deviation 4. If we take a random sample of 7 men age 30-60 years old. whe ...
2
votes
1answer
107 views

Deducing an optimal gambling strategy (using martingales).

Apologies in advance for the length, I tried being precise. Suppose a game where in each turn you can gamble a certain amount of money on the result of a fair coin toss. If the coin comes out tails ...
2
votes
4answers
124 views

Is it true that $\mathbb E[{\frac{X}{Y}]}={\frac{\mathbb E[X]}{\mathbb E[Y]}}$?

If $X$ and $Y$ are both random variables, does it hold $$\mathbb E\left[\frac{X}{Y}\right]={\frac{\mathbb E[X]}{\mathbb E[Y]}}$$ ??
4
votes
4answers
398 views

Probablity that 3 husbands sit next to their wives round a circular table

There are 3 couples sitting randomly round a 6-seater circular table. What is the probability that all the husbands and wives sit next to each other? My attempt: First wife, say, takes any of the ...
0
votes
0answers
164 views

To Find Expected Sum

I Have N objects to paint, ordered in a row and numbered form left to right starting from 1. There are total C colors, numbered from 0 to C-1. At the beginning all objects are colored in color with ...
0
votes
1answer
23 views

Finding $V(X)$ when you don't have a density/distribution function.

I just did the first part of this problem: You have a lot of $50$ items and are taking a sample size of $15$. In the lot $3$ items are defective. The lot is accepted if the number of defective items, ...
0
votes
1answer
21 views

Finding the $75$th percentile of a distribution.

So, I came across a couple of homework problems on finding percentiles. The first was: pdf of $X$ is $f(x)=\frac{10}{x^2}$ for $x\gt 10$, and $0$ otherwise. Finding the $75$th percentile here was ...
1
vote
1answer
64 views

Exponential Distribution question

I'm having some trouble understanding the mechanics of how to solve with this distribution. The question: The number of years that a washing machine functions is a random variable whose hazard rate ...
0
votes
2answers
35 views

Pick coloured balls from given urns

The contents of three given urns I, II and III are as follows 1 white, 2 black and 3 red 2 white, 1 black and 1 red 4 white, 5 black and 3 red One urn is chosen at random and two balls are drawn. ...
1
vote
1answer
56 views

Need help with a basic exercise about Markov chains

Suppose $\left\{ X_{n}\right\} _{n=1}^{\infty}$ is a Markov Chain taking real values. Are the following Markov Chains? $$Y_{n}=\sum_{i=1}^{n}X_{i} , Z_{n}=\left(X_{n},X_{n-1}\right)$$ Edit1 I ...
2
votes
3answers
19 views

Solution check for counting in a list

This problem involves lists made from the letters T,H,E,O,R,Y, with repetition allowed. How many 4-letter lists are there that don’t begin with T, or don’t end in Y ? Just want to make sure my ...
0
votes
1answer
26 views

Using the Weibull Distribution, derive $E(X^k)$

If $X$~WEI$(\theta,\beta)$, derive $E(X^k)$ assuming $k\gt-\beta$. Note that $X$~WEI$(\theta,\beta)=\frac{\beta}{\theta^{\beta}}x^{\beta -1}e^{-({x}/{\theta})^{\beta}}$ I am having a very difficult ...
2
votes
3answers
87 views

distribution of infinite sum of $\sum (2x_n -1)/2^n$

$\{X_n\}\sim\mathrm{Bernoulli}(\frac {1}{2})$ $$Y=\sum_{n=0} ^{\infty} \frac {2X_n -1}{2^n}$$ Find the distribution of $Y$ $X_n$ are independent
0
votes
1answer
51 views

solving Venn diagram

A record survey was carried out among $70$ teenagers. The choice was out of three records: $A,G,P$ the result showed that $52$ teenagers liked $A$, $29$ liked $G$, and $37$ liked $P$. It was also ...
0
votes
1answer
33 views

Find the PDF of Y given Y=X(2-X) and X's PDF

Suppose that the continuous random variable $X$ has probability density function $f_X(x)=\begin{cases}\frac{1}{2}x & \text{if } 0<x<2\\0&\text{otherwise}\end{cases}$ Let $Y=X(2-X)$. ...
3
votes
1answer
36 views

What is the distribution of $|X-Y|$ if both $X$ and $Y$ are $U(0,1)$?

I am trying to find the distribution of $Z = |X-Y|$ if both $X$ and $Y$ are uniform over $(0, 1)$ and independent. The answer I am getting is very close to the one given but I can't figure out why ...
0
votes
0answers
18 views

The distribution of ratio of two shifted gamma

I am wondering if anyone can help me to find the ratio of this distribution. Assume $S$ and $T$ are independent, where $S\sim Gamma(n-1/2, 4(1+\rho)\sigma^2)$ $S\sim Gamma(n-1/2, ...
2
votes
0answers
18 views

What happens to the sum of Bernouilli RVs divided by $ \sqrt(n)$

Suppose I have $$S=\frac {\sum_1^nX_i} {\sqrt(n)} $$ where $X_i$ is Bernouilli($p$) and $n$ goes to infinity. It doesn't look like it's approximately normal (the CLT doesn't apply since it's not ...
0
votes
0answers
33 views

Which of the following distributions could satisfy the law of large numbers?

I am working on the following question: A random variable Z is a choice of two RVs: X and Y, selected randomly, i.e., some $Z$ values were "originally" $X$'s, and the others were $Y$'s. For a ...
0
votes
1answer
40 views

Find the probability that the average of X and Z is greater than Y. Where X, Z, and Y are normal RVs.

Here is the exact statement: Suppose X,Y , and Z are independent random variables. X is a normal random variable with mean 5 and variance 16, Y is a normal random variable with mean 7 and variance ...
2
votes
1answer
43 views

Bessel's inequality for expected value

Let $X_1, X_2,\ldots$ be independent random variables with expected value $\mathbb{E}[X_i]=0$ and variance $V[X_i]=1$. Let $Y$ be another random variable, such that $\mathbb{E}[Y^2] < \infty$. I ...
0
votes
2answers
26 views

Probability Distributions Question about Freethrows

Bob has a 98% chance of making any freethrow. He throws until he misses. Determine the chance that: a) he misses for the first time on the 9th or 10th throw b) he misses for the first time on the ...
0
votes
2answers
24 views

Probability Distribution Question

On a football team there are 7 quarterbacks and 6 linemen. Coach selects 5 players. a) Determine the probability that he selects only 1 quarterback b) Determine the probability that he selects more ...
0
votes
2answers
27 views

Probability Distributions Question

A lottery corporation sells 100 000 tickets at \$3.00 per ticket. If the lottery has 2 first prizes worth \$20,000 each, 4 second prizes worth \$5000 each and 10 third prizes worth $500 each, ...
2
votes
1answer
21 views

Applying transition matrix to a probability vector seems to ruin its normalization

I had a little bit about stochastic processes during my "Statistical Physics" course and on my exam I got a problem with a Markov chain. My solution seems to be without computational mistakes (checked ...
3
votes
2answers
46 views

Traditional combination problem with married couples buying seats to a concert.

Three married couples have bought $6$ seats in a row for a concert. How many ways can they be seated if no man sits next to his wife. I have worked through this problem and have got the correct ...
0
votes
0answers
50 views

Finding the expected value of a random variable

Let: $$f(x) = \begin{cases} k(\frac23)^x, & \text{if }x \in \{1, 2, 3,\ldots\} \\[2ex] 0 & \text{elsewhere}\end{cases}$$ Find $k$: Because $x$ is countable, it is discrete. So, a $\sum$ is ...
2
votes
5answers
61 views

A machine has $9$ switches. Each switch has $3$ positions. How many different settings are possible?

A machine has $9$ switches. Each switch has $3$ positions. $(1)$ How many different settings are possible? Each switch has $3$ different settings and we have $9$ total. So, $3^9=19,683$ Now, the ...
3
votes
3answers
63 views

Probability a 9-digit number has the digits 2,4, and 6 next to each other.

The integers $1,2,3,....,9$ are arraned (at random) in a row, resulting in a $9$-digit integer (without replacement). What is the probability that: The result is even? $\frac49$ or $\frac{4(8!)}{9!}$ ...
1
vote
1answer
24 views

probability problem - expectation

A tourist wants to visit four cities: A, B, C and D. First he chooses one at random. If he chooses A he then randomly chooses among B, C and D. If he chooses B then he randomly chooses among A, C, D. ...
-1
votes
2answers
39 views

questions regarding probability homework

i have come up against a question i do not understand Box a has 5 balls one blue and 4 yellow box b has five balls three blue and 2 yellow find the probability the ball is yellow I am having problem ...
0
votes
0answers
24 views

German Tank Problem with Uniform Distribution

Let {X1, X2, …, Xn} be integers, generated by random round-off sampling from a uniform distribution U[0, b]. Now we want to estimate the parameters b, this is known as german tank problem in ...