Consider a Weibull distribution with the following pdf: f(x)= (Ɵ2/ Ɵ1)*(x/ Ɵ1)^( Ɵ2-1)*exp{-( x/ Ɵ1)^ Ɵ2}?

Consider a Weibull distribution with the following pdf:

f(x)= (Ɵ_{2}/ Ɵ_{1})*(x/ Ɵ1)^( Ɵ2-1)*exp{-( x/ Ɵ1)^ Ɵ2} For x>0, Ɵ1>0, Ɵ2>0

(a) if now Y=( x/ Ɵ1)^ Ɵ2. Show that Y follows an exponential distribution with a mean of 1.

Explain how to

(b) Explain how to generate a random variate from this Weibull distribution based on Y.

(c) Use part (a) to generate 500 random variates from this Weibull distribution when (Ɵ1, Ɵ2)=(3,3) and draw a histogram.

(d) Compare the histogram in part (c) with the actual pdf of Weibull (3,3).

(e) Now assume that this Weibull distribution is truncated at points (a,b) = (1,10). Generate 500 random variates from this trunacated Weibull distribution and compute the average.

(f) Compute the (theoretical expected value of this truncated population. Is the average in part(e) close to this expected value?

I am New in statistics and got this question as my homework. I tried my best but not able to solve this. Please help me both in Theoretical as well as Matlab coding for the above question