a) here as number of trails are independent and probability of head on each event is fixed ; therefore it is binomial distribution with parameter n=5 and p=0.5
hence probability mass function of X:
P(X=x)=
frm above P(X=0)= =0.03125
P(X=1)= =0.15625
P(X=2)=0.3125
P(X=3)=0.3125
P(X=4)=0.15625
P(X=5)=0.03125
probbaility distribution function F(x) of X is as follows:
0 | x<=0 | ||
0.03125 | 0<=x<1 | ||
0.1875 | 1<=x<2 | ||
F(x)= | 0.5 | 2<=x<3 | |
0.8125 | 3<=x<4 | ||
0.96875 | 4<=x<5 | ||
1 | x>=5 |
b)
P(realizing at least 3 heads out of 5) =P(X=3)+P(X=4)+P(X=5) =0.3125+0.15625+0.03125=0.5
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