Homework SoursePlease show all work Excel and minilab do not help Thank you
Please show all work. Excel and minilab do not help. Thank you in advance!
Let random variable x represent the number of heads when a fair coin is tossed three times.
(a) Construct a table describing the probability distribution.
(b)Determine the mean and standard deviation of x.(Round the answer to two decimal places)
Mean=
Standard Deviation=
| x | p(x) |
| 0 | |
| 1 | |
| 2 | |
| 3 |
Solution
X represent the number of heads
A fair coin is tossed three times. So, the outcomes is
HHH HHT HTT TTT TTH HTH THH THT
(a)
(b) The mean is
E(X)=xp=0*1/8+1*3/8+2*3/8+3*1/8=12/8=3/2=1.5
E(X2)=x2p=0*1/8+1*3/8+4*3/8+9*1/8=24/8=3
Var(X)=3-2.25=0.75
SD(X)=0.866
| x | p(x) |
| 0 | 1/8 |
| 1 | 3/8 |
| 2 | 3/8 |
| 3 | 1/8 |
