1.) Let X be a continuous random variable uniformly distributed on the interval [4,7]. let x be point within [4,7]. Use this info to solve parts a-b. Please be sure to also solve parts c-e, but parts c-e are independent questions.

a.) Compute the probability that the above random variable X takes values between 8.5 and 12.5.

b.) Compute the probability that the above random variable takes values between 3.5 and 6.5.

Solve part c-e

c.) Consider the following real function defined on the whole real line:

f(x)=cx^4, for x in [0,2], and 0 otherwise.

Find c such that this function represents the density of a random variable X.

d.) Consider a random variable X whose density is:

f(x) = ax + bx^2 for x in [0,1], and 0 otherwise. If E[X]=.6, find a and b.

e.) For the above X find P(X<1>