answer the question 1Suppose that a coin is flipped four tim

answer the question:

1.Suppose that a coin is flipped four times. Let X be a random vaiable that gives the total numbers of heads. Compute the following probability.

(a) P(X = 0) (b) P(X = 1) (c) P(X = 2) (d) P(X = 3) (e) P(X = 4)

2.Let G = (V, E) be a directed graph where V = {a, b, c, d, e, f, g} and E = {{a, d}, {b, c}, {b, d}, {b, f}, {c, e}, {d, c}, {d, d}, {e, d}, {e, f}, {f, b}, {f, e}, {f, f}}. Answer the following questions.

(a) What is the out-degree of b? (b) What is the in-degree of b?

(c) What is the out-degree of d? (d) What is the in-degree of d?

(e) What is the total degree of f?

Solution

Assume that coin is fair

p = prob for head =0.5

Each toss is independent and there are two outcomes

X - no of heads is binomial with (4,0.5)

a) P(X=0) = 0.0625

b) P(x=1) = 0.25

c) P(X=2) = 0.375

d) P(X=3) = 0.25

e) P(x=4) = 0.0625

a) outdegree of b = 3

b) in degree of b = 1

c) out degree of d = 2

d) in degree of d = 4

e) total degree of f = outdegree +in degree = 3+3=6