Respuesta :
Answer:
The random variable X follows a Binomial distribution.
[tex]E(X)=X\\SD(X)=\sqrt{\frac{X(300-X)}{300}}[/tex]
Step-by-step explanation:
The random variable X defined as the number of children who have been diagnosed with ASD.
The random sample of children selected is of size n = 300.
The probability of children diagnosed with ASD is, [tex]P(X)=p=\frac{X}{300}[/tex].
A children diagnosed with ASD is independent of all the others.
The random variable X follows a Binomial distribution.
[tex]X\sim Bin(n=300, p=\frac{X}{300})[/tex]
The expected value of X is:
[tex]E(X)=np=300\times \frac{X}{300}=X[/tex]
The standard deviation of X is:
[tex]SD(X)=\sqrt{np(1-p)}=\sqrt{300\times \frac{X}{300}[1-\frac{X}{300}]}=\sqrt{\frac{X(300-X)}{300}}[/tex]
