Answer:
The probability distribution of X is shown below.
Step-by-step explanation:
The random variable X = number of female puppies in a litter.
The size of the litter is, n = 5.
The probability of a puppy being a male or a female is same, i.e.
P (X) = p = 0.50.
The random variable X follows a Binomial distribution with parameters n = 5 and p = 0.50.
The probability mass function of a Binomial distribution is:
[tex]P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...[/tex]
Compute the probability of the event X = 0 as follows:
[tex]P(X=0)={5\choose 0}0.50^{0}(1-0.50)^{5-0}\\=1\times1\times 0.03125\\=0.03125[/tex]
Compute the probability of the event X = 1 as follows:
[tex]P(X=1)={5\choose 1}0.50^{1}(1-0.50)^{5-1}\\=5\times0.50\times 0.0625\\=0.15625[/tex]
Compute the probability of the event X = 2 as follows:
[tex]P(X=2)={5\choose 2}0.50^{2}(1-0.50)^{5-2}\\=10\times0.25\times 0.125\\=0.3125[/tex]
Compute the probability of the event X = 3 as follows:
[tex]P(X=3)={5\choose 3}0.50^{3}(1-0.50)^{5-3}\\=10\times0.125\times 0.25\\=0.3125[/tex]
Compute the probability of the event X = 4 as follows:
[tex]P(X=4)={5\choose 4}0.50^{4}(1-0.50)^{5-4}\\=5\times0.0625\times 0.50\\=0.15625[/tex]
Compute the probability of the event X = 5 as follows:
[tex]P(X=5)={5\choose 5}0.50^{5}(1-0.50)^{5-5}\\=1\times0.03125\times 1\\=0.03125[/tex]
The probability distribution table is shown below.
