Advertisements
Advertisements
Question
Define Mathematical expectation in terms of discrete random variable
Advertisements
Solution
Let X be a discrete random variable with probability mass function (p.m.f) P(x).
Then, its expected value is defined by E(X) = `sum_x x"p"(x)`
In other words,
If x1, x2, x3,…… xn are the different values of X, and p(x1), p(x2) …..p(xn) are the corresponding probabilities, then E(X) = x1 p(x1) + x2 p(x2) + x3 p(x3) +… xn p(xn)
APPEARS IN
RELATED QUESTIONS
Four fair coins are tossed once. Find the probability mass function, mean and variance for a number of heads that occurred
A commuter train arrives punctually at a station every half hour. Each morning, a student leaves his house to the train station. Let X denote the amount of time, in minutes, that the student waits for the train from the time he reaches the train station. It is known that the pdf of X is
`f(x) = {{:(1/30, 0 < x < 30),(0, "elsewhere"):}`
Obtain and interpret the expected value of the random variable X
A lottery with 600 tickets gives one prize of ₹ 200, four prizes of ₹ 100, and six prizes of ₹ 50. If the ticket costs is ₹ 2, find the expected winning amount of a ticket
Choose the correct alternative:
A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is
The following table is describing about the probability mass function of the random variable X
| x | 3 | 4 | 5 |
| P(x) | 0.2 | 0.3 | 0.5 |
Find the standard deviation of x.
Let X be a continuous random variable with probability density function
`"f"_x(x) = {{:(2x",", 0 ≤ x ≤ 1),(0",", "otherwise"):}`
Find the expected value of X
Choose the correct alternative:
E[X – E(X)]2 is
Choose the correct alternative:
An expected value of a random variable is equal to it’s
Prove that if E(X) = 0, then V(X) = E(X2)
Prove that V(aX) = a2V(X)
