Question

A continuous random variable has a probability distribution function such that it takes on values

in the interval from 2 to 10 with equal likelihood.

a) Sketch the pdf described above and the cumulative distribution.

b) What is the probability that a random variable will take on a value between 4.04 and 7.96?

c) What is the probability that a random variable will take on a value less than 7?

d) What is the probability that a random variable will equal 8?

Answer 1

a)

here for uniform distribution parameter a =2 and b=10

pdf :f(x)=1/(b-a) =

1/8

CDF: F(x)=(x-a)/(b-a) =

(x-2)/8

b)

probability =

P(4.04<X<7.96)=

(7.96-4.04)/(10-2)=

0.4900

c)

probability =

P(X<7)=

(7-2)/(10-2)=

0.6250

d)

probability that a random variable will equal 8 =0 (As for continuous distribution , point probability is 0)