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