Question

For random variable X, X Bi( 300, . 1) find probabilities : P( X > 35), P( 28 CX < 31) Let Yi, Y2,..., Yso be a sequence of exponentially distributed random variable with parameter λ=.4, and Y=Σ Y/40. Find P(Y<2) 40 7 projector-1&messa google.com/mail/u/0/#inbox/FMfcgxwBVCzcfjWVpqNzGmrwWBgGqrN? gePartid=0.2

  

which way is the simplest to solve this problem? is there other way than using gamma function ? please add the different ways to solve this problem. Thank you !!!

Answer 1

6)
X follow binomial distribution
n = 300 and p = 0.1

You can use normal approximation

mean = np = 300 * 0.1 = 30

sd =sqrt(npq) = sqrt(300 * 0.1 * 0.9) = 5.1962

Z = (X - mean)/sd = (X - 30)/5.1962

P(X > 35) = P(X >= 35.5)   { contnuity correction}

= P (Z > (35.5 - 30)/5.1962)

= P (Z>1.06)

=0.1446

b)

P(28 < X< 31)

= P(28.5 <= X< = 30.5)

= P ( −0.29<Z<0.1 )

=0.1539

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