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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1answer
23 views
Veany Eat chocolate chips
In a cookie jar, there are 6 chocolate chip cookies and 8 oatmeal cookies. Veany takes out the cookies one at a time and proceeds to eat them. The probability that the 7th cookie that Veany eats is a ...
1
vote
2answers
11 views
integrating using student t distribution
Evaluate the integral
$\int_0^\infty\frac{1}{1+x^2}dx$
using the Student t distribution.
I don't know where to start. I am assuming that I can't just do regular integration. I don't know how I am ...
0
votes
1answer
4 views
Finding the moment-generating function for a function of $X$
Let $X_1,\dots,X_n$ be independent random variables with a normal distribution having mean $1$ and variance $2$. Find the moment generating function for $n^{-1/2}(S_n-n)$.
Umm. Our book doesn't have ...
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0answers
7 views
Model for stock market changes over the day
A common model for stock returns is as follows: the number of
trades $N$ of stock XXX in a given day has a Poisson distribution with parameter $\lambda$. At each trade, say the $i$’th trade, the ...
1
vote
1answer
16 views
probability of a board containing a certain number of accountants
A corporate board contains twelve members. The board decides to create a five-person Committee
to Hide Corporation Debt. Suppose four members of the board are accountants. What is the probability that ...
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votes
2answers
25 views
Probability of missiles on target
The captain of a Navy gunboat orders a volley of 25 missiles to be fired at random along a five-hundred-foot stretch of shoreline that he hopes to establish as a beachhead. Dug into the beach is a ...
1
vote
1answer
22 views
If $a_n \rightarrow 1$, does $X_n \overset{p}{\rightarrow} X$ implies $a_n X_n \overset{p}{\rightarrow} X$?
The title pretty much sums it up.
I'm trying to prove that $S_n^2 \overset{p}{\rightarrow} \sigma^2$. So far, I have:
$S_n^2 = \frac{n}{n-1} \frac{1}{n} \sum_{i=1}^n X_i^2 - \frac{n}{n-1} ...
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votes
1answer
13 views
Independence between Uniform distribution and Exponential distribution question
I am trying to solve the following problem and I am having a great deal of difficulty in a number of areas. Help would be greatly appreciated!
Let me state the problem first.
If $X$ is uniformly ...
1
vote
1answer
15 views
Limits of Integration for marginal pdf
I just had a small question as something is bothering me.
I am trying to find the marginal pdf of the following joint pdf:
$f(x,y) = (1/8)(y^2 - x^2)e^{-y}$ where $-y \le x \le y$, $0 < y < ...
0
votes
2answers
41 views
probability of hitting $1/n$ with $n$ tries, and applying it
Disclaimer, I'm a computer person, not a math person, so surely I'm not going to use the proper math lingo. I apologize in advance. Feel free to edit to make this question more readable to others. ...
1
vote
4answers
51 views
Shooting game - a probability question
In a shooting game, the probability for Jack to hit a target is 0.6.
Suppose he makes 8 shots, find the probabilities that he can hit the
target in more than 5 shots.
I find this question in ...
3
votes
1answer
38 views
Safes and keys probability puzzle
I have $100$ keys and $100$ safes. Each key opens only one safe, and each safe is opened only by one key. Every safe contains a random key. 98 of these safes are locked. What's the probability that I ...
1
vote
2answers
22 views
Finding variance given expected value
How would one find the variance of a random variable, $X$ given that it is composed of say two dependent random variables $Y_1$ and $Y_2$ (so $X = Y_1 + Y_2$), each with expected value of .5 and ...
6
votes
1answer
58 views
Find the value of a function with definite integrals
I am trying to understand a paper of Maynard Smith (1974), that connects biology with game theory. I don't want to overwhelm you with useless stuff, but I have this definite integrals:
...
1
vote
0answers
12 views
Hypothesis testing problem of Normal distributions.
Consider the following Hypothesis Testing problem:
Hypothesis $H_0$ : $X \sim N(\mu_0, \sigma_0)$. Mean $\mu_0$ is known but only upper and lower bounds on $\sigma_0$ are known.
Hypothesis $H_1$ : ...
