Advertisements
Advertisements
Question
If X ~ B (n, p) and E(X) = 6 and Var (X) = 4.2, then find n and p.
Solution
Given, X ~ B (n, p) and E(X) = 6 and Var (X) = 4.2
Now, `(E(X))/(u(X)) = (np)/(npq)`
⇒ `6/4.2 = 1/q`
⇒ q = `4.2/6` = 0.7
Since, p + q = 1
⇒ p + 0.7 = 1
⇒ p = 0.3
Now E(X) = np
⇒ 6 = n × 0.3
⇒ n = `6/0.3 = 60/3` = 20
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 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.
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 ______
Let X ~ B(n, p) if E(X) = 5, Var(X) = 2.5, then p(X < 1) is equal to ______.
