If X is a binomial variate with parameters n and p, where 0 < p < 1 such that frac{text{P(X = r)}}{text{P(X = n -

Q: If X is a binomial variate with parameters n and p, where 0 < p < 1 such that $\frac{\text{P(X = r)}}{\text{P(X = n - r})}$ is independent of n and r, then p equals:

Consider, $\text{P(X = r})=\text{kP(X = n}-\text{r})$ Using $\text{ }^{\text{n}}\text{C}_{\text{r}}=\text{ }^{\text{n}}\text{C}_{\text{n}-\text{r}},\text{q}=1-\text{p}$ $\text{p}^{\text{r}}\text{q}^{\text{n}-\text{r}}=\text{kp}^{\text{n}-\text{r}}\text{q}^{\text{r}}$ $\text{p}^{\text{r}}(1-\text{p})^{\text{n}-\text{r}}=\text{kp}^{\text{n}-\text{r}}(1-\text{p})^{\text{r}}$ $\text{P}^{2\text{r}-\text{n}}=\text{k}(1-\text{p})^{2\text{r}-\text{n}}$ $\big(\frac{\text{p}}{\text{q}}\big)^{2\text{r}-\text{n}}=\text{k}$ when $\text{p = q}$ then $\text{k}=1$ $\Rightarrow\text{p = q}=\frac{1}{2}$

M.C.Q (1 Marks)

GSEB - English Medium

If X is a binomial variate with parameters n and p, where 0 < p < 1 such that $\frac{\text{P(X = r)}}{\text{P(X = n - r})}$ is independent of n and r, then p equals:

A$\frac{1}{2}$
B$\frac{1}{3}$
C$\frac{1}{4}$
D$\text{None of these}$

STD 12 Science
Maths
Probability
Exemplar

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Download App

Similar Questions

1
Choose the correct answer from the given four options.
The probability distribution of a discrete random variable X is given below:

$\text{X}$ $2$ $3$ $4$ $5$

$\text{P}(\text{X})$ $\frac{5}{\text{k}}$ $\frac{7}{\text{k}}$ $\frac{9}{\text{k}}$ $\frac{11}{\text{k}}$

The value of k is:
View Solution
2
Mark the correct alternative in the following question:
The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is:
View Solution
3
A fair coin is tossed 100 times. The probability of getting tails an odd nimber of times is:
View Solution
4
Mark the correct alternative in the following question:Which one is not a requirement of a binomial dstribution?
View Solution
5
A coin is tossed 10 times. The probability of getting exactly six heads is:
View Solution
6
Choose the correct answer from the given four options. Two dice are thrown. If it is known that the sum of numbers on the dice was less than $6,$ the probability of getting a sum $3,$ is:
View Solution
7
Let $X$ denote the number of times heads occur in $n$ tosses of a fair coin. If $P(X = 4), P(X = 5)$ and $P(X = 6)$ are in $AP,$ the value of $n$ is:
View Solution
8
If A and B are two events such that P(A) = 0.4, P(B) = 0.3 and $\text{P}(\text{A}\cup\text{B})=0.5,$ then $\text{P}(\overline{\text{B}}\cap\text{A})$ equals.
View Solution
9
If A and B are two independent events with $\text{P(A)}=\frac{3}{5}$ and $\text{P(B)}=\frac{4}{9},$ then $\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$ equals,
View Solution
10
Choose the correct answer in each of the following:
If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, then
View Solution

$\text{X}$	$2$	$3$	$4$	$5$
$\text{P}(\text{X})$	$\frac{5}{\text{k}}$	$\frac{7}{\text{k}}$	$\frac{9}{\text{k}}$	$\frac{11}{\text{k}}$

Download our appand get started for free

Similar Questions

Download our app
and get started for free