A discrete random variable X takes value from 1 to 5 with probabilities as shown in the table. A student calculate the mean of X as 3.5 and her teacher calculates the variance to X as 1.5 which of the following statement is true?

K 1 2 3 4 5

P(X = K) 0.1 0.2 0.4 0.2 0.1

Both the student and the teacher are right

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Both the student and the teacher are wrong

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The student is wrong but the teacher is right

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The student is right but the teacher is wrong

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Solution

The correct option is B Both the student and the teacher are wrong
$μ = E (x)$
$= \sum p_{i} x_{i} = p_{1} x_{1} + p_{2} x_{2} + . . . + p_{5} x_{5}$
= 3
$E (x^{2}) = \sum p_{i} x_{i}^{2}$
$= (0.1) \times (1)^{2} + (0.2) \times (2)^{2} + (0.4) \times (3)^{2} + (0.2) \times (4)^{2} + (0.1) \times (5)^{2}$
= 10.2

So $V a r (x) = E (x^{2}) - (E (x))^{2} = 10.2 - (3)^{2} = 1.2$

Hence both are wrong.

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A discrete random variable X takes value from 1 to 5 with probabilities as shown in the table. A student calculate the mean of X as 3.5 and her teacher calculates the variance to X as 1.5 which of the following statement is true? K 1 2 3 4 5 P(X = K) 0.1 0.2 0.4 0.2 0.1

The correct option is B Both the student and the teacher are wrong μ=E(x) =∑pixi=p1x1+p2x2+...+p5x5 = 3 E(x2)=∑pix2i =(0.1)×(1)2+(0.2)×(2)2+(0.4)×(3)2+(0.2)×(4)2+(0.1)×(5)2 = 10.2 So Var(x)=E(x2)−(E(x))2=10.2−(3)2=1.2 Hence both are wrong.

A discrete random variable X takes value from 1 to 5 with probabilities as shown in the table. A student calculate the mean of X as 3.5 and her teacher calculates the variance to X as 1.5 which of the following statement is true?

K 1 2 3 4 5

P(X = K) 0.1 0.2 0.4 0.2 0.1