Question

Question 23 :
Two coins are tossed simultaneously. Let X denote number of heads then v(X) is
O 1
02
O 4
O 1/2​

Answer 1

Given : Two coins are tossed simultaneously.

X denote number of heads

To Find :  V(X)

1

2

4

1/2

Solution:

Two coins are tossed simultaneously.

Probability Head = 1/2

Probability Tail = 1/2

X denote number of heads

P(0)  =   (1/2)(1/2)  = 1/4    (TT)

P(1)  = (1/2)(1/2) + (1/2)(1/2) = 1/2   ( HT , TH)

P(2)  = (1/2)(1/2)  =  1/4     (HH)

Mean Expected number of Head E(X) =  ∑ xP  = 0 * P(0) + 1 *P(1)  + 2 * P(2)

= 0 (1/4)  +  1( 1/2)  + 2(1/4)

=  0  + 1/2  + 1/2

= 1

Mean Expected number of Head  E(X) =  1

∑ x²P  =  0² * P(0) + 1² *P(1)  + 2² * P(2)

= 0  + 1/2  + 1

= 3/2

Var(X)  =  ∑x²p - (∑xp)²

=  3/2  - (1)²

= 3/2 - 1

= 1/2

V(X)  =1/2

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