Math, asked by girlzrlier123, 3 months ago

a die is tossed four times. A success is getting 1 or 2 on a toss find the mean and variance of the number of success​

Answers

Answered by anonymous1510
0

Let x be the random variable denoting the number of times an odd number (the number of successes) when a die is tossed twice.

Then x takes the values 0,1,2

Let P(X=0) be probability of getting no odd number (both times showing even).

∴P(X=0)=
6
3

×
6
3

=
4
1



Let P(X=1) be probability of getting odd number once.

∴P(X=1)=2C
1


6
3

×
6
3

=
6
6

×
6
3

=
2
1



Let P(X=2) be probability of getting odd number twice.

∴P(X=2)=
6
3

×
6
3

=
4
1



Thus the probability distribution of X is given by
X=x x=0 x=1 x=2
P(X=x)
4
1


2
1


4
1


We know that mean E(X)=∑x
i

P
i

=0×
4
1

+1×
2
1

+2×
4
1



∴E(X)=0+
2
1

+
2
1

=1

Thus mean E(X)=1.

We know that var(X)=E(X
2
)−[E(X)]
2


E(X
2
)=∑x
i
2

P
i

=0×
4
1

+1
2
×
2
1

+2
2
×
4
1



∴E(X
2
)=0+
2
1

+4×
4
1

=
2
3



Thus var(X)=
2
3

−[1]
2
=
2
3

−1=
2
1



Hence mean is 1 and variance is
2
1
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