Respuesta :
Answer:
(a) The value of P (X = 1, Y = 2) is 0.1583.
(b) The value of P (X + Y = 1) is 0.1055.
Step-by-step explanation:
It is provided that:
[tex]X\sim Bin(n=4,p=0.25)\\\\Y\sim Bin(n=4,p=0.50)[/tex]
The variables X and Y are independent random variables.
The probability mass function of a Binomial distribution is:
[tex]P(U=u)={n\choose u}(p)^{u}(1-p)^{n-u};\ u=0,1,2,3...[/tex]
(a)
Compute the value of P (X = 1, Y = 2) as follows:
[tex]P(X=1,Y=2)=[{n\choose x}(p_{x})^{x}(1-p_{x})^{n-x}]\times [{n\choose y}(p_{y})^{y}(1-p_{y})^{n-y}][/tex]; Independent
[tex]=[{4\choose 1}(0.25)^{1}(1-0.25)^{4-1}]\times [{4\choose 2}(0.50)^{2}(1-0.50)^{4-2}]\\\\=0.422\times 0.375\\\\=0.15825\\\\\approx 0.1583[/tex]
Thus, the value of P (X = 1, Y = 2) is 0.1583.
(b)
Compute the value of P (X + Y = 1) as follows:
[tex]P(X+Y=1)=P(X=0,Y=1)+P(X=1,Y=0)[/tex]
[tex]=\{[{4\choose 0}(0.25)^{0}(1-0.25)^{4-0}]\times [{4\choose 1}(0.50)^{1}(1-0.50)^{4-1}]\}\\+\{[{4\choose 1}(0.25)^{1}(1-0.25)^{4-1}]\times [{4\choose 0}(0.50)^{0}(1-0.50)^{4-0}]\}\\\\=(0.3164\times 0.25)+(0.422\times0.0625)\\\\=0.0791+0.0264\\\\=0.1055[/tex]
Thus, the value of P (X + Y = 1) is 0.1055.
