###### Advertisements

###### Advertisements

The probability mass function for X = number of major defects in a randomly selected

appliance of a certain type is

X = x | 0 | 1 | 2 | 3 | 4 |

P(X = x) | 0.08 | 0.15 | 0.45 | 0.27 | 0.05 |

Find the expected value and variance of X.

###### Advertisements

#### Solution

`E(X)=sumx_i.P(x_i)`

`=0(0.08)+1(0.15)+2(0.45)+3(0.27)+4(0.05)`

`=0+0.15+0.9+0.81+0.2=2.06`

`E(X^2)=sumx_i^2.P(x_i)`

`=0(0.08)+1^2(0.15)+2^2(0.45)+3^2(0.27)+4^2(0.05)`

`=0 + 0.15 + 1.8 + 2.43 + 0.8=5.18`

`Var(X)=E(X^2)-[E(X)]^2`

`=5.18-(2.06)^2`

`=5.18-4.2436`

`=0.9364`

#### APPEARS IN

#### RELATED QUESTIONS

Given is X ~ B(n, p). If E(X) = 6, and Var(X) = 4.2, find the value of n.

The difference between mean and variance of a binomial distribution is 1 and the difference of their squares is 11. Find the distribution.

Let X ~ B(n, p) if n = 10, E(X) = 5, find p and Var(X).

Let X ~ B(n, p) if E(X) = 5 and Var(X) = 2.5, find n and p.

If a fair coin is tossed 10 times and the probability that it shows heads 5 times.

**State whether the following is True or False :**

The p.m.f. of a r.v. X is P(x) = `(2x)/("n"("n" + 1))` , x = 1, 2, ……. n

= 0 ,otherwise

Then E(x) = `(2"n" + 1)/(3)`

For X ~ B(n, p), if V(X) = 2.4 and p = 0.4, then n = ______.

Given that X ~ B(n = 10, p), E(X) = 8, then value of p = ______

A die is thrown. If X denotes the number of positive divisors of the outcomes, then find the range of random variable X

A r.v. X ~ B(n, p). If the values of mean and variance of X are 18 and 12 respectively, then find total number of positive values of X.

Let the p.m.f. of r.v. X be P(x) = `""^4"C"_x (5/9)^x (4/9)^(4 - x)`, x = 0, 1, 2, 3, 4. Find E(X) and Var(X)

**Choose the correct alternative:**

The variance of a Binomial distribution is given by ______

Find the expected value and variance X using the following p.m.f.

x |
– 2 | – 1 | 0 | 1 | 2 |

P(x) |
0.2 | 0.3 | 0.1 | 0.15 | 0.25 |

Let X ~ B(n, p). If n = 10 and E(X) = 5, using the following activity find p and Var(X)

**Solution:** E(X) = `square = 5 square "p" = square, "q" = square`

Var(X) = `square`

The mean and variance of a binomial distribution are 2 and 1 respectively, then the probability of getting exactly three successes in this distribution is ______.

If the mean and variance of a binomial variate X are 14 and 10 respectively, then the probability that X takes a value greater than or equal to 1 is ______

If X ~ B (n, p) and E(X) = 6 and Var (X) = 4.2, then find n and p.

Let X ~ B(n, p) if E(X) = 5, Var(X) = 2.5, then p(X < 1) is equal to ______.