Answer to Question #185357 in Statistics and Probability for Jeeshan

Question

 State whether the following statements are true or false. Give a short proof or a counter 

example in support of your answers: (10) 

 

 (a) Poisson distribution is a limiting case of binomial distribution for n p, 1

→ → ∞ and 

np ∞.

→

 (b) For two independent events A and B, if P(A) = 2.0 and P(B) = ,4.0 then 

(A∩ B) = .6.0

 (c) If H0

: P ≤ 6.0 and X ~ B(n, p)n -known and p unknown and 1 0 H :µ = µ where 

X ~ N

2 2

(µ,σ )σ unknown, then H0

 and H1

 are simple null hypothesis. 

 (d) Frequency density of a class for any distribution is the ration of total frequency to 

class width. 

 (e) If X and Y are independent r.v.s with M (t) X

 and M (t) Y

 as their m.gf’s 

respectively, then M (t) M (t)M t).( X +Y = X Y

2) A,B and C are three events. Express the following 

Answer 1

(a) True: The Poisson distribution is a limiting case of the binomial distribution which arises when the number of trials n increases indefinitely whilst the product μ = np, which is the expected value of the number of successes from the trials, remains constant.

(b)False:

As $P(A\cup B)=P(A)+P(B)-P(A\cap B)$

$P(A\cap B)=2+0.6-1=1.6$

(c) False: As the mean of the mean of the binomal istribution is less as mentioned in the hypothesis.

(d) True:Frequency density of a class for any distribution is the ration of total frequency to 

class width. 

(e)True: As X and Y are independent events So the moment generating function M(X+Y)=M(XY)

M.( X +Y) = M(X Y)