Mathematics: If a random sample of 300 children is selected, let X be the number of these children who have been diagnosed with ASD. What distribution does X follow? What is the expected value and standard deviation of X?

If a random sample of 300 children is selected,

taishaun

20.01.2022

The random variable X follows a Binomial distribution.

$E(X)=X\\SD(X)=\sqrt{\frac{X(300-X)}{300}}$

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, $P(X)=p=\frac{X}{300}$ .

A children diagnosed with ASD is independent of all the others.

The random variable X follows a Binomial distribution.

$X\sim Bin(n=300, p=\frac{X}{300})$

The expected value of X is:

$E(X)=np=300\times \frac{X}{300}=X$

The standard deviation of X is:

$SD(X)=\sqrt{np(1-p)}=\sqrt{300\times \frac{X}{300}[1-\frac{X}{300}]}=\sqrt{\frac{X(300-X)}{300}}$

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nathaliapachon1254

30.05.2023

Step-by-step explanation:

Use triangle congruency:

BC=EC, AC=DC - Given

m∠DCE = m∠ACB because they are vertical angles

Therefore ΔABC ≅ ΔDEC because of Side-Angle-Side congruency

AB=DE because corresponding parts of congruent triangles are also congruent (CPCTC)

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