Question

Assume a Poisson distribution with-5.8. Find the following probabilities. b.X-1 с. X>1

Answer 1

(1)

(a)

(b)

P(X<1) = P(X=0)

5.85.80 0.0030x1-0.0030 P(X = 0) =-O!

So,

P(X<1)= 0.0030

(c)

P(X>1) = 1 - [P(X=0) + P(X=1)]

= 1 - (0.0030 + 0.0176)

= 0.9794

(d)
P(X1) = P(X = 0)+ P(X=1)

= 0.0030 + 0.0176

= 0.0206

(2)

Formula:

$p=rac{E}{N}$

E(X) = np

(a)

n = 3, N = 9, E = 7

Substituting, we get:

7 p 0.7778

(i)

Mean is given by:

E(X) = np= 3 × 0.7778 = 2.3333

(ii)

Variance is given by:

So,

Standard Deviation is given by:

(b)

n = 5, N = 8, E = 3

Substituting, we get:

(i)

Mean is given by:

(ii)

Variance is given by:

5 × 0.375(1-0.375)(8-5) 8-1 5 × 0.375 × 0.625 × 3 7 Var(X) = = 0.5022

So,

Standard Deviation is given by:

V0.5022-0.7087

(c)

n = 6, N = 14, E = 3

Substituting, we get:

$p=rac{3}{14}=0.2143$

(i)

Mean is given by:

(ii)

Variance is given by:

So,

Standard Deviation is given by:

$sqrt{0.6217}=0.7885$

(d)

n = 4, N = 9, E = 4

Substituting, we get:

$p=rac{4}{9}=0.4444$

(i)

Mean is given by:

(ii)

Variance is given by:

4 × 0.4444(1-0.4444) (9-4) 9-1 4 × 0.4444 × 0.5556 × 5 Var(X) = 0.6173

So,

Standard Deviation is given by:

$sqrt{0.6173}=0.7857$