expected value

Let $X$ be a random variable which takes values in the set $\{1,2,3,4,5,6,7,8\}$. Further, $\operatorname{Pr}(X=1)=\operatorname{Pr}(X=2)=\operatorname{Pr}(X=5)=\operatorname{Pr}(X...

The unit interval (0,1) is divided at a point chosen uniformly distributed over (0,1) in R into two disjoint subintervals. The expected length of the subinterval that contains 0.4...

The unit interval $(0,1)$ is divided at a point chosen uniformly distributed over $(0,1)$ in $R$ into two disjoint subintervals. The expected length of the subinterval that contain...

Let x and y be random variables, not necessarily independent, that take real values in the interval [0,1]. Let z = xy and let the mean values of x, y, z be x̄, ȳ, z̄, respectively....

In an examination, a student can choose the order in which two questions (QuesA and QuesB) must be attempted. - If the first question is answered wrong, the student gets zero marks...

The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component...

Let T be a full binary tree with 8 leaves. (A full binary tree has every level full). Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected...

Suppose you break a stick of unit length at a point chosen uniformaly at random. Then the expected length of the shorter stick is __________________.

Each of the nine words in the sentence "The Quick brown fox jumps over the lazy dog" is written on a separate piece of paper. These nine pieces of paper are kept in a box. One of t...

When a coin is tossed, the probability of getting a Head is p, 0 < p < 1. Let N be the random variable denoting the number of tosses till the first Head appears, including the toss...

An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the tails are independent, the expected number of tosses are

A point is randomly selected with uniform probability in the X-Y plane within the rectangle with corners at (0, 0), (1, 0), (1, 2) and (0, 2). If p is the length of the position ve...

An examination paper has 150 multiple-choice questions of one mark each, with each question having four choices. Each incorrect answer fetches-0.25 mark. Suppose 1000 students choo...

Consider the following algorithm for searching for a given number x in an unsorted array A[1..n] having n distinct values: 1. Choose an i uniformly at random fro 1..n; 2. If A[i]=x...

Let X and Y be two exponentially distributed and independent random variables with mean $$\alpha $$ and $$\beta $$, respectively. If Z = min (X, Y), then the mean of Z is given by