A continuous random variable *Y *has pdf (probability density function)

f

(*y*) = 2eky , y > 0

1/ 6, − 6 < y < −3

(a)

Determine the value of the constant *k*. Then sketch the pdf.

Finally, derive and sketch *Y*'s cdf (cumulative distribution function).

(b)

Find *Y*'s mean, variance and standard deviation.

(c)

Find *Y*'s mode and median.

** **

Hi there,

I have done part of the question and want to cross check the answers i got.

a) k= -4

cdf

F(y) = 0 y<-6

(1/6)y -6<y<-3

{ [(1/6) (3- 3e^(-4y) +y]} y>0

b) E(Y) = (169/16) + [ (-y/4)e^ (-4y) - ((1/16)e^(-4y))

Please, correct me if I am wrong

Cheers