Advertisements
Advertisements
प्रश्न
Consider a random variable X with p.d.f.
f(x) = `{(3x^2",", "if" 0 < x < 1),(0",", "otherwise"):}`
Find E(X) and V(3X – 2)
उत्तर
Let X be the random variable
`"E"(x^2) = int_(-oo)^oo x"f"(x) "d"x`
`"E"(x) = int_0^1 x(3x^2) "d"x`
= `int_0^1 x(3x^3) "d"x`
= `3[x^4/4]_0^1`
= `3/4[x^4]_0^1`
= `3/4[1 - 0]`
`"E"(x) = 3/4`
`"E"(x^2) = int_(-oo)^oo x^2"f"(x) "d"x`
= `int_0^1 x^2 (3x^2) "d"x`
= `int_0^1 3x^4 "d"x`
= `3(x^5/5)_0^1`
= 3/5[x^5]_0^1`
= `3/5[1 - 0]`
= `3/5`
Var(x) = `"E"(x^2) - ["E"(x)]^2`
= `33/5 - (3/4)^2`
= `3/5 - 9/16`
= `(48 - 45)/80`
Var(x) = `3/80`
`"v"(3x - 2) = (3)^2"Var"(x)` .......`{because "v"(""x + "b") = "a"^2"v"(x)}`
= `9(3/80)`
∴ `"V"(3x - 2) = 27/80`
APPEARS IN
संबंधित प्रश्न
Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values of the random variable X and number of points in its inverse images
A six sided die is marked ‘2’ on one face, ‘3’ on two of its faces, and ‘4’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the values of the random variable and number of points in its inverse images
A continuous random variable X has the following distribution function
F(x) = `{{:(0",", "if" x ≤ 1),("k"(x - 1)^4",", "if" 1 < x ≤ 3),(1",", "if" x > 3):}`
Find k
A continuous random variable X has the following distribution function
F(x) = `{{:(0",", "if" x ≤ 1),("k"(x - 1)^4",", "if" 1 < x ≤ 3),(1",", "if" x > 3):}`
Find the Probability density function
Explain the terms probability density function
State the properties of distribution function.
Choose the correct alternative:
A variable that can assume any possible value between two points is called
Choose the correct alternative:
If c is a constant, then E(c) is
Choose the correct alternative:
In a discrete probability distribution, the sum of all the probabilities is always equal to
The probability density function of a continuous random variable X is
f(x) = `{{:("a" + "b"x^2",", 0 ≤ x ≤ 1),(0",", "otherwise"):}`
where a and b are some constants. Find a and b if E(X) = `3/5`
