Let a random variable X have a binomial distr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given that the mean of the binomial distribution is $np = 8$ and the variance is $npq = 4$.Dividing the variance by the mean,we get $q = \frac{npq

Vedclass · Accepted Answer

$137$

Vedclass · Answer

(B) Given that the mean of the binomial distribution is $np = 8$ and the variance is $npq = 4$.Dividing the variance by the mean,we get $q = \frac{npq}{np} = \frac{4}{8} = \frac{1}{2}$.Since $p + q = 1$,we have $p = 1 - \frac{1}{2} = \frac{1}{2}$.Substituting $p = \frac{1}{2}$ into $np = 8$,we get $n 	imes \frac{1}{2} = 8$,which implies $n = 16$.The probability mass function is $P(X = r) = ^{16}C_r (\frac{1}{2})^r (\frac{1}{2})^{16-r} = ^{16}C_r (\frac{1}{2})^{16}$.We need to find $P(X \le 2) = P(X=0) + P(X=1) + P(X=2)$.$P(X \le 2) = \frac{^{16}C_0 + ^{16}C_1 + ^{16}C_2}{2^{16}}$.Calculating the combinations: $^{16}C_0 = 1$,$^{16}C_1 = 16$,and $^{16}C_2 = \frac{16 	imes 15}{2} = 120$.Summing these values: $1 + 16 + 120 = 137$.Thus,$P(X \le 2) = \frac{137}{2^{16}}$.Comparing this with $\frac{k}{2^{16}}$,we get $k = 137$.

Let a random variable $X$ have a binomial distribution with mean $8$ and variance $4$. If $P(X \le 2) = \frac{k}{2^{16}}$,then $k$ is equal to

Similar Questions

Three rods of the same dimensions have thermal conductivities $3 K, 2 K$,and $K$. They are arranged as shown in the figure below. The temperature of the junction in the steady state is:

$BX_3 + NH_3 \xrightarrow{R.T} BX_3 \cdot NH_3 + \text{Heat of adduct formation } (\Delta H)$. The numerical value of $\Delta H$ is found to be maximum for:

Assertion: One molal aqueous solution of glucose contains $180 \text{ g}$ of glucose in $1 \text{ kg}$ of water.
Reason: $A$ solution containing one mole of solute in $1000 \text{ g}$ of solvent is called a one molal solution.

The component of vector $\vec{A} = 2\hat{i} + 3\hat{j}$ along the vector $\vec{B} = \hat{i} + \hat{j}$ is:

$A$ clock pendulum made of invar has a period of $0.5 \, s$ at $20^{\circ} C$. If the clock is used in a climate where the temperature averages to $30^{\circ} C$, how much time does the clock lose in each oscillation? (For invar, $\alpha = 9 \times 10^{-7} /{ }^{\circ} C$, $g = \text{constant}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module