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
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"):}`
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
Choose the correct alternative:
A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is
In investment, a man can make a profit of ₹ 5,000 with a probability of 0.62 or a loss of ₹ 8,000 with a probability of 0.38. Find the expected gain
What are the properties of Mathematical expectation?
What do you understand by Mathematical expectation?
The number of miles an automobile tire lasts before it reaches a critical point in tread wear can be represented by a p.d.f.
f(x) = `{{:(1/30 "e"^(- x/30)",", "for" x > 0),(0",", "for" x ≤ 0):}`
Find the expected number of miles (in thousands) a tire would last until it reaches the critical tread wear point
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:
Probability which explains x is equal to or less than a particular value is classified as
Choose the correct alternative:
A discrete probability function p(x) is always non-negative and always lies between
