My books and notes fail me , i would greatly appreciate help and explanation of the following problems.

a)

The PDF of a continuous random variable, (X) is shown below:

f(x) = ke-2x, x > 0,

f(x) = 0, otherwise.

(i)Calculate the value of the constant, k.

(ii)Find P(1 £ X £ 2).

b)

The PDF of a continuous random variable, (X), is shown below:

f(x) = cx-1/2, 0 < x < 9,

f(x) = 0, otherwise.

(i)Calculate the value of the constant, c.

(ii)Find the expected value of X.

(iii)Find the value of the variance of X.

Thanks!