Answer:
The answer to each point is below
Step-by-step explanation:
We will solve point by point:
a) We have to:
Random variable X = number of heads
Let, H => heads, T => tails
b) We have that the combinations are
TTT, TTH, THT, THH, HTT, HTH, HHT, HHH
Number of Heads (X) 0 1 2 3
Probability (P) 1/8 3/8 3/8 1/8
c) attached the histogram.
d) We have the following:
Mean = E (X) = 0 * 1/8 + 1 * 3/8 + 2 * 3/8 + 3 * 1/8
m = 1.5
The mean is 1.5
e) E (X ^ 2) = 0 * 1/8 + 12 * 3/8 + 22 * 3/8 + 32 * 1/8 = 3
Variance = E (X ^ 2) - (E (X)) ^ 2
Var = 3 - (1.5) ^ 2
Var = 0.75
The variance is 0.75
f) standard deviation = (Var) ^ (1/2) = (0.75) ^ (1/2) = 0.866
sd = 0.866
the standard deviation is 0.866
g) P (2 or more heads) = 3/8 + 1/8 = 0.5
The probability is 50%
h) P (two heads) = 3/8 = 0.375
It is likely that out of 8 times of 3 flips, 3 times we can observe two heads out of 3, therefore it is not unusual.
