Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Let x be a continuous random variable.
In the probability density function,
Expected Value E(x) = `int_(-oo)^oo x"f"(x) "d"x`
Here E(x) = `int_0^1 x(2x) "d"x = int_0^1 2x^2 "d"x`
= `2[x^3/3]_0^1`
= `2/3[x^3]_0^1`
= `2/3 [1 - 0]`
= `2/3`
∴ E(x) = `2/3`
APPEARS IN
संबंधित प्रश्न
Two balls are drawn in succession without replacement from an urn containing four red balls and three black balls. Let X be the possible outcomes drawing red balls. Find the probability mass function and mean for X
Choose the correct alternative:
Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins ₹ 36, otherwise he loses ₹ k2, where k is the face that comes up k = {1, 2, 3, 4, 5}. The expected amount to win at this game in ₹ 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
How do you defi ne variance in terms of Mathematical expectation?
A person tosses a coin and is to receive ₹ 4 for a head and is to pay ₹ 2 for a tail. Find the expectation and variance of his gains
Choose the correct alternative:
Probability which explains x is equal to or less than a particular value is classified as
Choose the correct alternative:
A probability density function may be represented by
Choose the correct alternative:
If p(x) = `1/10`, x = 10, then E(X) is
Choose the correct alternative:
An expected value of a random variable is equal to it’s
