Advertisements
Advertisements
Question
How do you defi ne variance in terms of Mathematical expectation?
Advertisements
Solution
The variance of X is defined by
Var(X) = `sum[x - "E"("x")]^2 "p"(x)`
If X is discrete random variable with probability mass function p(x).
Var(X) = `int_-oo^oo [x - "E"("X")]^2 "f"_x (x) "d"x`
If X is continuous random variable with probability density function fx (x).
APPEARS IN
RELATED QUESTIONS
For the random variable X with the given probability mass function as below, find the mean and variance.
`f(x) = {{:((4 - x)/6, x = 1"," 2"," 3),(0, "otherwise"):}`
Four fair coins are tossed once. Find the probability mass function, mean and variance for a number of heads that occurred
The probability density function of the random variable X is given by
`f(x) = {{:(16x"e"^(-4x), x > 0),(0, x ≤ 0):}`
find the mean and variance of X
Choose the correct alternative:
A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is
Choose the correct alternative:
Four buses carrying 160 students from the same school arrive at a football stadium. The buses carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on that bus. Then E(X) and E(Y) respectively are
Choose the correct alternative:
On a multiple-choice exam with 3 possible destructive for each of the 5 questions, the probability that a student will get 4 or more correct answers just by guessing 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 random variable and Y = 2X + 1. What is the variance of Y if variance of X is 5?
Choose the correct alternative:
E[X – E(X)]2 is
Choose the correct alternative:
`int_(-oo)^oo` f(x) dx is always equal to
