Advertisements
Advertisements
Question
If µ and σ2 are the mean and variance of the discrete random variable X and E(X + 3) = 10 and E(X + 3)2 = 116, find µ and σ2
Advertisements
Solution
Given E(X + 3) = 10
E(aX + b) = aE(X) + b
E(X + 3) = 10
⇒ E(X) + 3 = 10
⇒ µ = E(X) = 7
E(X + 3)2 = 116
E(X2 + 6X + 9) = 116
E(X2) + 6E(X) + 9 = 116
E(X2) + 6(7) + 9 = 116
E(X2) = 65
σ² = Var (X)
= E(X2) – [E(X)]2
= 65 – 49
= 16
APPEARS IN
RELATED QUESTIONS
For the random variable X with the given probability mass function as below, find the mean and variance.
`f(x) = {{:(1/10, x = 2"," 5),(1/5, x = 0"," 1"," 3"," 4):}`
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:
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:
If P(X = 0) = 1 – P(X = 1). If E[X] = 3 Var(X), then P(X = 0) is
Choose the correct alternative:
If X is a binomial random variable with I expected value 6 and variance 2.4, Then P(X = 5) is
Find the expected value for the random variable of an unbiased die
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
How do you defi ne variance in terms of Mathematical expectation?
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?
Choose the correct alternative:
Value which is obtained by multiplying possible values of a random variable with a probability of occurrence and is equal to the weighted average is called
Choose the correct alternative:
Probability which explains x is equal to or less than a particular value is classified as
Choose the correct alternative:
Which of the following is not possible in probability distribution?
Choose the correct alternative:
`int_(-oo)^oo` f(x) dx is always equal to
Choose the correct alternative:
A listing of all the outcomes of an experiment and the probability associated with each outcome is called
Choose the correct alternative:
An expected value of a random variable is equal to it’s
Choose the correct alternative:
The distribution function F(x) is equal to
Prove that V(aX) = a2V(X)
