Advertisements
Advertisements
Question
The probability density function of a continuous random variable X is
f(x) = `{{:(a + bx^2",", 0 ≤ x ≤ 1),(0",", "otherwise"):}`
where a and b are some constants. Find Var(X)
Advertisements
Solution
`"E"(x^2) = int_(-oo)^oo x^2"f"(x) "d"x`
= `int_0^1 ("a"x^2 + "b"x4) "d"x`
= `{3/5 (x^3/3) + 6/5[x^5/5]}_0^1`
= `[1/5 (x^3) + 6/25 (x^5)]_0^1`
= `[1/5 (1) + 6/25(1)] - [0]`
= `1/5 + 6/25`
= `(5 + 6)/25`
= 11
Var(x)= `"E"(x^2) - ["E"(x)]`
= `1/25 - (3/5)^2`
= `11/25 - 9/5`
= `(11 - 9)/25`
Var(x) = `2/25`
APPEARS IN
RELATED QUESTIONS
In a pack of 52 playing cards, two cards are drawn at random simultaneously. If the number of black cards drawn is a random variable, find the values of the random variable and number of points in its inverse images
The discrete random variable X has the probability function
| X | 1 | 2 | 3 | 4 |
| P(X = x) | k | 2k | 3k | 4k |
Show that k = 0 1
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
The length of time (in minutes) that a certain person speaks on the telephone is found to be random phenomenon, with a probability function specified by the probability density function f(x) as
f(x) = `{{:("Ae"^((-x)/5)",", "for" x ≥ 0),(0",", "otherwise"):}`
Find the value of A that makes f(x) a p.d.f.
Explain the terms probability Mass function
Explain the terms probability density function
Explain the terms probability distribution function
What are the properties of continuous random variable?
Choose the correct alternative:
If the random variable takes negative values, then the negative values will have
The probability function of a random variable X is given by
p(x) = `{{:(1/4",", "for" x = - 2),(1/4",", "for" x = 0),(1/2",", "for" x = 10),(0",", "elsewhere"):}`
Evaluate the following probabilities
P(|X| ≤ 2)
