Question

7, Random variable X has a hypergeometric distribution with N= 25, n = 4, and K = 4. Determine the following: a) E(X) b) V(X) c) P(X- 1) d) P(X-4) e) P(X2

Answer 1

Sample size,     n =    4
No. of events of interest in population    , k =   4
Population size   , N =   25
a)

mean = E(X) = n(k/N) =    0.64
b)

variance = VAR(X) = nk/N(1 - k/N)((N-n)/(N-1))    0.4704
c)

it is hypergeometric distribution          
          
P(X=x) =C(k,x)*C(N-k,n-x)/C(N,n)          
P( X =   1   ) = C(    4   ,   1   ) * C (    21   ,    3   ) / C (    25   ,   4   ) = 0.4206

d)

P( X =   4   ) = C(    4   ,   4   ) * C (    21   ,    0   ) / C (    25   ,   4   ) = 0.0001

e) P(X≤2) = 1 - P(X=3) - P(X=4)

P( X =   3   ) = C(    4   ,   3   ) * C (    21   ,    1   ) / C (    25   ,   4   ) = 0.0066

so, P(X≤2) = 1-0.0066-0.0001 = 0.9933