1.) Let X be a continuous random variable uniformly distributed on the interval [4,7]. let x be point within [4,7]. Please answer parts a-e given this information. Please show all work and all steps for all parts a-e to get marked as a helpful answer.

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.

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>