Question

. The average monthly rainfall (AMR) in inches is a random variable with the cumulative distribution function (cdf):\

a. Determine the probability that the AMR is less than 1.5 inches.

b. Determine the probability the AMR is between 1.5 and 2 inches.

c. What is the median AMR? d. Determine the equation describing the probability density function (pdf), f(x)

4 F(x) = .16, otherwise

Answer 1

a)

P(X<1.5)=F(1.5) =(1.5)⁴/16 =0.316406

b)

P(1.5<X<2)=F(2)-F(1.5)=(2)⁴/16-(1.5)⁴/16 =1-0.316406 =0.683594

c)

let median be a;

hence F(a)=0.5

a⁴/16 =0.5

a=1.681793

d)

here pdf f(x)=(d/dx)F(x)=(d/dx)*(x⁴/16)

f(x)=x³/4    for 0 <x< 2