# Tagged Questions

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### Problem calculating the average power of a vector?

I am calculating the average power of a vector. I would like to compare the final expression with the simulation. However, they are not equal. Please help me to point out which steps are wrong. Thank ...
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### Extension to Classical Coupon Collectors Problem

If there's n different coupons. Instead of ordering coupons one-by-one until you collect all n coupons as in the traditional 'Coupon Collector Problem', what if the coupons came in packs of m coupons. ...
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### Extension to the Coupon Collector Problem

If there's n different coupons. Instead of ordering coupons one-by-one until you collect all n coupons as in the traditional 'Coupon Collector Problem', what if the coupons came in packs of m coupons. ...
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### Expected Value of Local Maxima and Local Minima

Recently I came across this question: Given a random permutation of integers 1, 2, 3, …, n with a discrete, uniform distribution, find the expected number of local maxima. (A number is a local maxima ...
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### Random number x probability in interval [0,10]

So lets say $x=10*rand()$, so x will be equal to a random number on the interval [0,10]. So what is the probability of $2x+1$ rounding to $5$. So one can come up with $4.5<=2x+1<5.5$. Is that ...
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### Covariance problem.

The experiment is a three hat experiment with the following probabilities: $\frac15$ for $(1,2,3)$, $(1,3,2)$, $(2,1,3)$ and $(3,2,1)$, and $\frac1{10}$ probability for $(2,3,1)$ and $(3,1,2)$. Find ...
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### Expected value vs using method of indicator

I am having a hard time understanding the difference between getting the Expected value by finding the mean E(X)=np and using the method of indicator to find the expected value. For example if we ...
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### Calculating the distribution of random variables and the expected value/mean of a random variable?

I'm not sure whether or not I picked the correct distribution method and calculated the distribution correctly. Here is the problem: Consider Bob, an absent-minded student. Bob has a set of 5 ...
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### Question about a random variable/probability example

Say $X_1$ is a random variable equivalent to a flip of a fair six sided dice. say $X_2$ is also a random variable equivalent to a flip of a fair six sided dice. and say that $X = X_1 + X_2$ How ...
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### Bernoulli distribution vs the probability mass function

What is the difference between the two? They seem to mean the same thing to me. The probability mass function can be used to find the probability of getting a tail from a coin flip: X{1 ...
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### Discrete random variables problem

I don't know how to answer the following question: Argue that if $X$ and $Y$ are nonnegative random variables, then $E[\max(X,Y)] \leq E[X] + E[Y]$
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### Random variable $X$ inducing a distribution on $V$

I have been learning about discrete probability and found a somehow confusing (to me) definition of distribution of a random variable $X$ on a set $V$. The definition of a Random variable $X$:  ...
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### Finding unknown values from discrete probabilities.

(I am confused here with the limits. It says x = 0,1,2,3... So what is my end limit her? Thanks.)
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### Proving a variable as discrete random (confusing question)

A box contains 3 white and 3 black marbles. In a game, 3 marbles are randomly selected from the box. The score (X) is equivalent to the getting of 10 white marbles. Show that X is a discrete random ...
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### Expected value of index of the minimum element in an array

I'm stuck the following assignment: What is the expected value of the index of the minimum element in an array of n distinct integer that are randomly ordered? I think it should be something like: ...
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### Expected number of Diamonds in a 5-card hands

What would be the correct answer for expected number of diamonds in a 5-card hands? I am thinking as follow: Let $X_i = 1$ if the i-th card is diamond, or $0$ otherwise. $X_i = (1 \times P($i-th ...
### Ignoring $\max$ for discrete random variables
Let $X,Y,Z$ be independent discrete random variables with $X\sim\text{Bin}(6,7/8),$ $Y\sim\text{Bin}(5,7/8)$ and $Z\sim\text{Geo(1/4)}$. Futhermore let $M:=\max(X+Y,Z)$. Compute ...