Question

There are 4 cards numbered 1,3,5 and 7,one number card.two cards are drawn at random without replacement.let x denote the sum of the numbers on the two drawn cards.find the mean and variance of x

Answer 1

Answer:

Mean = 8, Standard Deviation = 20/3

Step-by-step explanation:

Let X be the random variable which takes the sum of the numbers on the 2 drawn cards,

Given cards numbered are 1,3,5 and 7.

So since there are 4 , so chosing 2 can be done in 4C2 ways =6.

Now, the possible combinations are (1,3) (1,5) (1,7) (3,5) (3,7) (5,7) each with probability 1/6.

So X=sum of 2 numbers, takes the values 4,6,8,8,10,12

Hence 8 occurs with probability 1/3 and others with 1/6 probability.

Mean of random variable(μ)is defined as ∑xf(x) where x represents the values ranom variable takes and f(x) are the respective probabilities,

μ = 4*1/6 +6*1/6 +8*1/3 +10*1/6 +12*1/6

=8------(*)

Variance is defined as σ²=∑(x-μ)²f(x),

On simplification we get

σ² = 20/3----(**)