Probability Distribution - Probability Density Function (P.D.F.)

The pdf of a random variable X is

f(x) = 3(1 - 2x²), 0 < x < 1

      = 0   otherwise

The P`(1/4 < "X" < 1/3)` = ?

If the probability density function of a random variable X is given as

then F(0) is equal to

If random variable waiting time in minutes for bus and probability density function of x is given by

f(x) = `{{:(1/5",", 0 ≤ x ≤ 5),(0",", "otherwise,"):}`

then probability of waiting time not more than 4 minutes is equal to ______.

If the probability density function continuous random variable X is

f(x) = k(1 - x₂); 0 < x < 1
      = 0  ;    otherwise

Then P`(0 < X < 1/2)` = ?

If the p.d.f. of a continuous random variable X is given as

`f(x)=x^2/3` for -1< x<2

       =0   otherwise

then c.d.f. fo X is

(A) `x^3/9+1/9`

(B) `x^3/9-1/9`

(C) `x^2/4+1/4`

(D) `1/(9x^3)+1/9`

The following is the p.d.f. (ProbabiIity Density Function) of a continuous random variable X :

`f(x)=x/32,0<x<8`

= 0 otherwise

(a) Find the expression for c.d.f. (Cumulative Distribution Function) of X.

(b) Also find its value at x = 0.5 and 9.

Given the p. d. f. (probability density function) of a continuous random variable x as :

 `f(x)=x^2/3, -1`

         = 0 , otherwise

Determine the c. d. f. (cumulative distribution function) of x and hence find P(x < 1), P(x ≤ -2), P(x > 0), P(1 < x < 2)

The p.d.f of a random variable x is given by

f(x) = `1/"4a"`, 0 < x < 4a, (a > 0)

= 0, otherwise

and `"P"(x < "3a"/2) = "kp"(x > "5a"/2)` then k = ?