English
Tamil Nadu Board of Secondary EducationHSC Commerce Class 12

How do you defi ne variance in terms of Mathematical expectation? - Business Mathematics and Statistics

Advertisements
Advertisements

Question

How do you defi ne variance in terms of Mathematical expectation?

Sum

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).

shaalaa.com
Mathematical Expectation
  Is there an error in this question or solution?
Chapter 6: Random Variable and Mathematical expectation - Exercise 6.2 [Page 141]

APPEARS IN

Samacheer Kalvi Business Mathematics and Statistics [English] Class 12 TN Board
Chapter 6 Random Variable and Mathematical expectation
Exercise 6.2 | Q 9 | Page 141

RELATED QUESTIONS

For the random variable X with the given probability mass function as below, find the mean and variance.

`f(x) = {{:(2(x - 1), 1 < x ≤ 2),(0, "otherwise"):}`


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


The time to failure in thousands of hours of an electronic equipment used in a manufactured computer has the density function
`f(x) = {{:(3"e"^(-3x), x > 0),(0, "eleswhere"):}`
Find the expected life of this electronic equipment


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


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


Define Mathematical expectation in terms of discrete random variable


Choose the correct alternative:

If X is a discrete random variable and p(x) is the probability of X, then the expected value of this random variable is equal to


Choose the correct alternative:

Which of the following is not possible in probability distribution?


Choose the correct alternative:

E[X – E(X)] is equal to


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×