Check the solution to "How do you find the mean of the..."

Yahir Haas

Answered question

2022-01-28

How do you find the mean of the random variable x?
X= 5,10,15,20,25
P(x) = 1/5, 1/5 , 1/5, 1/5, 1/5
What is the variance and standard deviation of the random variable x?
What is the standard deviation of the random variable x?

Answer & Explanation

sineurosi0f

Beginner2022-01-29Added 14 answers

mean E(X)=15
Var(X)=50
sd=7.07
Explanation:
For a probability distribution

E (X) = \sum_{a l l x} x P (X = x)

...(1)
in this case we have

E (X) = 5 \times \frac{1}{5} + 10 \times \frac{1}{5} + 15 \times \frac{1}{5} + 20 \times \frac{1}{5} + 25 \times \frac{1}{5}

E(X)=1+2+3+4+5
E(X)=15
the variance is calculated by

V a r (X) = E (X^{2}) - E (X)

...(2)
where

E (X^{2}) = \sum_{a l l x} x^{2} P (X = x)

...(3)

E (X^{2}) = 5^{2} \times \frac{1}{5} + 10^{2} \times \frac{1}{5} + 15^{2} \times \frac{1}{5} + 20^{2} \times x \frac{1}{5} + 25^{2} \times \frac{1}{5}

E (X) = \frac{1}{5} (25 + 100 + 225 + 400 + 625)

E (X^{2}) = 275 .

V a r (X) = 275 - 15^{2} = 275 - 225 = 50

s d = \sqrt{V a r (X)} = \sqrt{50} = 7.07

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