Respuesta :
Answer:
P (X = 0) = 0.001 P (X = 4) = 0.205 P (X = 8) = 0.044
P (X = 1) = 0.010 P (X = 5) = 0.246 P (X = 9) = 0.010
P (X = 2) = 0.044 P (X = 6) = 0.205 P (X = 10) = 0.001
P (X = 3) = 0.117 P (X = 7) = 0.117
Step-by-step explanation:
In case of a Binomial experiment there are n repeated trials and each trial has only two outcomes: Success or Failure. The probability of success is denoted by p and the probability of failure is (1 - p).
The binomial experiment follows a discrete probability distribution with PDF :
[tex]P(X =x)={n\choose x}p^{x}(1-p^{n-x}[/tex];x = 0, 1, 2, 3...
Given: n = 10 and p = 0.50
(1)
The value of P (X = 0) is:
[tex]P(X =0)={10\choose 0}(0.50)^{0}(1-0.50)^{10-0}=1\times 1\times 0.00097\approx0.001[/tex]
(2)
The value of P (X = 1) is:
[tex]P(X =1)={10\choose 1}(0.50)^{1}(1-0.50)^{10-1}=10\times 0.50\times 0.00195\approx0.010[/tex]
(3)
The value of P (X = 2) is:
[tex]P(X =2)={10\choose 2}(0.50)^{2}(1-0.50)^{10-2}=45\times 0.25\times 0.00391\approx0.044[/tex]
(4)
The value of P (X = 3) is:
[tex]P(X =3)={10\choose 3}(0.50)^{3}(1-0.50)^{10-3}=120\times 0.125\times 0.007813\approx0.117[/tex]
(5)
The value of P (X = 4) is:
[tex]P(X =4)={10\choose 4}(0.50)^{4}(1-0.50)^{10-4}=210\times 0.0625\times 0.015625\approx0.205[/tex]
(6)
The value of P (X = 5) is:
[tex]P(X =5)={10\choose 5}(0.50)^{5}(1-0.50)^{10-5}=252\times 0.03125\times 0.03125\approx0.246[/tex]
(7)
The value of P (X = 6) is:
[tex]P(X =6)={10\choose 6}(0.50)^{6}(1-0.50)^{10-6}=210\times 0.015625\times 0.0625\approx0.205[/tex]
(8)
The value of P (X = 7) is:
[tex]P(X =7)={10\choose 7}(0.50)^{7}(1-0.50)^{10-7}=120\times 0.007813\times 0.125\approx0.117[/tex]
(9)
The value of P (X = 8) is:
[tex]P(X =8)={10\choose 8}(0.50)^{8}(1-0.50)^{10-8}=45\times 0.00391\times 0.25\approx0.044[/tex]
(10)
The value of P (X = 9) is:
[tex]P(X =9)={10\choose 9}(0.50)^{9}(1-0.50)^{10-9}=10\times 0.00195\times 0.50\approx0.010[/tex]
(11)
The value of P (X = 10) is:
[tex]P(X =10)={10\choose 10}(0.50)^{10}(1-0.50)^{10-10}=1\times 0.00097\times 1\approx0.001[/tex]
