Please answer the following questions from the information given: 1. Compare h(x

Question

Please answer the following questions from the information given:

1.     Compare h(x) with f(x) for each of the three distributions by doing the following: For each distribution let x = 0 and x =1 compare h(x) and f(x) for those two x values. h(x) = height of the histogram bar centered at x; f(x) = P(X=x)

2.     Look at the pmf’s for b(10,.1) and b(10,.9). State the obvious relation between the two distributions.

Histogram of b(10,1), b(10,.5), b(10,.9) Binomial with n = 10 and p = 0.1 Binomial with n = 10 and p-0.9 b(10.5) 0.3 (x=x 0.4 0.3 0.2 0.1 0 0.348678 1 0.387420 2 0.193710 3 0.057396 4 0.011160 5 0.001488 6 0.000138 7 0.000009 8 0.000000 9 0.000000 10 0.000000 0 0.000000 1 0.000000 2 0.000000 3 0.000009 4 0.000138 5 0.001488 6 0.011160 7 0.057396 8 0.193710 9 0.387420 10 0.348678 034 0.2 0.18 0.9 0.14 0.19 Scale 07 0.07 0.05 0.02 0.01 0.0 0.0 0 123 4 5 6 7 8 9 10 0 1 2 3 4 5 67 89 10 0.4 031 0.3 0.18 0.2 0.1 0.0 0.05 001 0 1 2 3 45 6 7 8 9 10

Explanation / Answer

1. At x=0,

for b(10,0.1)

density = 0.34

for b(10,0.5)

density = 0

for b(10,0.9)

density = 0

so, only for b(10,0.1) it has some height.

for x=1:

for b(10,0.1)

density = 0.48

for b(10,0.5)

density = 0.02

for b(10,0.9)

density = 0

height of b(10,0.1) is maximum.

2. b(10,.1) and b(10,.9) have perfect negative association.

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