40)

the area of the region bounded by the probability density

function f(x) = - 2x + 2, the x-axis, the vertical line x=0.5 and

the vertical line x=1. [Draw a picture of this region in the

plane. Note: Our probability density function f(x) = - 2x + 2 is a

straight line with an x intercept at (1,0) and a y-intercept at

(0,2).] This region in the plane is a right triangle with horizontal

leg of length 0.5 and vertical leg of length 1. Since the area of

a triangle is equal to .5*b*h, the area is equal to (0.5*1)/2=0.

25 .

for n=0,1,2,3,4,5 and 6. [Note that for all n, pk(1-p)n-k = 1/26]

P(0)=1*1/2^6 = 0.015625

P(1) =6*1/2^6 = 0.09375

P(2) =15*1/2^6 = 0.234375

P(3) =20*1/2^6 = 0.3125

P(4) =15*1/2^6 = 0.234375

P(5) =6*1/2^6 = 0.09375

P(6) =1*1/2^6 = 0.015625

P(0)=1*0.25^6 ≈ 0.0002

P(1) =6*0.75*0.25^5 ≈ 0.0044

P(2) =15*0.75^2*0.25^4 ≈ 0.0330

P(3) =20*0.75^3*0.25^3 ≈ 0.1318

P(4) =15*0.75^4*0.25^2 ≈ 0.2966

P(5) =6*0.75^5*0.25 ≈ 0.3550

P(6) =1*0.75^6 ≈ 0.1780