Find the binomial distribution whose mean is 5 and variance 10 3 … - Vidyadip

Question

Find the binomial distribution whose mean is 5 and variance $\frac{10}{3}.$

✓

Answer

Let n and p be the parameters of binomial distribution.
Given, $\text{Mean = np}=5\dots(1)$
$\text{Variance = npq}=\frac{10}{3}\dots(2)$
Dividing (2) by (1)
$\frac{\text{npq}}{\text{np}}=\frac{\frac{10}{3}}{5}$
$\text{q}=\frac{2}{3}$
So, $\text{p}=1-\text{q}$ [Since p + q = 1]
$=1-\frac{2}{3}$
$\text{p}=\frac{1}{3}$
Put the value of p in equation (1),
$\text{np}=5$
$\text{n}=5\times3$
$\text{n}=15$
Hence, the binomial distribution is given by
$\text{P(X = r})=\text{ }^{\text{n}}\text{c}_{\text{r}}\text{p}^{\text{r}}\text{q}^{\text{n}-\text{r}}$
$\text{P(X = r})=\text{ }^{15}\text{c}_{\text{r}}\big(\frac{1}{3}\big)^{\text{r}}\big(\frac{2}{3}\big)^{15-\text{r}}$
$\text{r}=0,1,2,\dots15$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Probability→Probability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

It is known that 60% of mice inoculated with a serum are protected from a certain disease. If 5 mice are inoculated, find the probability that.

none contract the disease.
more than 3 contract the disease.

Find the coordinates of the foot of the perpendicular from the point (1, 1, 2) to the plane 2x - 2y + 4z + 5 = 0. Also, find the length of the perpendicular.

A particle moves along the curve $y = x^2 + 2x$. At what point(s) on the curve are the x and y coordinates of the particle changing at the same rate?

If $x^y+y^x=b^a+a^b$ then find $\frac{d y}{d x}$.

Evaluate the definite integral in Exercise:
$\int^{\frac{\pi}{3}}\limits_{\frac{\pi}{6}}\frac{\sin\text{x}+\cos\text{x}}{\sqrt{\sin2\text{x}}}\text{dx}$

If P is a point and ABCD is a quadrilateral and $\overrightarrow{\text{AP}}+\overrightarrow{\text{PB}}+\overrightarrow{\text{PD}}=\overrightarrow{\text{PC}}$, show that ABCD is a parallelogram.

Find the equation of the tangent line to the curve $y = x^2 - 2x + 7$ which is perpendicular to the line $5y - 15x = 13.$

Solve the following determinant equations:
$\begin{vmatrix}3\text{x}-8&3&3\\3&3\text{x}-8&8\\3&3&3\text{x}-8\end{vmatrix}=0$

A company produces two types of goods, A and B, that require gold and silver. Each unit of type A requires 3gm of silver and 1 gm of gold while that of type B requires 1 gm of silver and 2gm of gold. The company can produce 9gm of silver and 8gm of gold. If each unit of type A brings a profit of Rs. 40 and that of type B Rs. 50, find the number of units of each type that the company should produce to maximize the profit. What is the maximum profit?

Three persons A, B and C apply for a job of Manager in a Private Company. Chances of their selection (A, B and C) are in the ratio $1 : 2 : 4$. The probabilities that A, B and C can introduce changes to improve profits of the company are $0.8, 0.5$ and $0.3$, respectively. If the change does not take place, find the probability that it is due to the appointment of C.