Respuesta :
Answer:
S = {0,2,3,4}
P(X=0) = 0.573 , P(X=2) = 0.401 , P(x=3) = 0.025, P(X=4) = 0.001
Mean = 0.879
Standard Deviation = 1.033
Step-by-step explanation:
Let the number of people having same birth month be = x
The number of ways of distributing the birthdays of the 4 men = (12*12*12*12)
The number of ways of distributing their birthdays = 12⁴
The sample space, S = { 0,2,3,4} (since 1 person cannot share birthday with himself)
P(X = 0) = [tex]\frac{12P4}{12^{4} }[/tex]
P(X=0) = 0.573
P(X=2) = P(2 months are common) P(1 month is common, 1 month is not common)
P(X=2) = [tex]\frac{3C2 * 12P2}{12^{4} } + \frac{4C2 * 12P3}{12^{4} }[/tex]
P(X=2) = 0.401
P(X=3) = [tex]\frac{4C3 * 12P2}{12^{4} }[/tex]
P(x=3) = 0.025
P(X=4) = [tex]\frac{12}{12^{4} }[/tex]
P(X=4) = 0.001
Mean, [tex]\mu = \sum xP(x)[/tex]
[tex]\mu = (0*0.573) + (2*0.401) + (3*0.025) + (4*0.001)\\\mu = 0.879[/tex]
Standard deviation, [tex]SD = \sqrt{\sum x^{2} P(x) - \mu^{2}} \\SD =\sqrt{ [ (0^{2} * 0.573) + (2^{2} * 0.401) + (3^{2} * 0.025) + (4^{2} * 0.001)] - 0.879^{2}}[/tex]
SD = 1.033
