Advertisements
Advertisements
Question
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"):}`
Advertisements
Solution
Probability mass function
| x | 1 | 2 | 3 |
| F(x) | `1/2` | `1/3` | `1/6` |
Mean: `mu = "E"("X")`
= `sum x f(x)`
= `1 xx 1/2 + 2 xx 1/3 + 3 xx 1/6`
= `1/2 + 2/3 + 3/6`
= `10/6`
= 1.67
Variance: `"E"("X"^2)`
= `1^2 xx 1/2 + 2^2 xx 1/3 + 3^2 xx 1/6`
= `1/2 + 4/3 + 9/6`
= `20/6`
= 3.33
Var (X) = E(X2) – [E(X)]2
= 3.33 – (1.67)2
= 3.33 – 2.79
= 0.54
APPEARS IN
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"):}`
For the random variable X with the given probability mass function as below, find the mean and variance.
`f(x) = {{:(1/2 "e"^(x/2), "for" x > 0),(0, "otherwise"):}`
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
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
Let X be a continuous random variable with probability density function
f(x) = `{{:(3/x^4",", x ≥ 1),(0",", "otherwise"):}`
Find the mean and variance of X
How do you defi ne variance in terms of Mathematical expectation?
Define Mathematical expectation in terms of discrete random variable
State the definition of Mathematical expectation using continuous random variable
In a business venture a man can make a profit of ₹ 2,000 with a probability of 0.4 or have a loss of ₹ 1,000 with a probability of 0.6. What is his expected, variance and standard deviation of profit?
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:
Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0.29, 0.40, 0.35. Profit per unit is 0.50 paisa then expected profits for three days are
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:
A probability density function may be represented by
Choose the correct alternative:
`int_(-oo)^oo` f(x) dx is always equal to
Choose the correct alternative:
The distribution function F(x) is equal to
Prove that if E(X) = 0, then V(X) = E(X2)
Prove that V(aX) = a2V(X)
