4.7 Distribution of sum of independent uniform RVs. A RV Y is the sum of 500 independent and identically distributed RVs X1, X2, . . . , X500. Each Xi is uniformly distributed over (1, 2). Find the mean and variance of Y . Give an approximate distribution or PDF of Y and justify your answer. What is the probability that Y is larger than 750

Let X1,X2,...,Xn be i.i.d. random variables with expected value EXi=μ<∞ and variance 0<Var(Xi)=σ2<∞. Then, the random variable

Zn=X¯¯¯¯−μσ/n−−√=X1+X2+...+Xn−nμn−−√σ

converges in distribution to the standard normal random variable as n goes to infinity, that is

limn→∞P(Zn≤x)=Φ(x), for all x∈R,

where Φ(x) is the standard normal CDF.

Step-by-step explanation:

the answer is 510

step-by-step explanation:

15 • 13 = 195

15 • 12 = 180

15 • 5 = 75

12 • 5 = 60

195 + 180 = 375

375 + 75 = 450

450 + 60 = 510

44

step-by-step explanation: