A fair n (n 1) faced die is rolled repeated | vedclass

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

Question

(D) Let $X$ be the number of tosses required. The probability of getting a number less than $n$ in a single toss is $p = \frac{n-1}{n}$.The probabilit

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(D) Let $X$ be the number of tosses required. The probability of getting a number less than $n$ in a single toss is $p = \frac{n-1}{n}$.The probability of getting the number $n$ in a single toss is $q = 1 - p = \frac{1}{n}$.The random variable $X$ follows a geometric distribution where the probability of success is $p = \frac{n-1}{n}$.The mean of a geometric distribution is given by $E[X] = \frac{1}{p}$.Given that the mean is $\frac{n}{9}$,we have $\frac{1}{p} = \frac{n}{9}$.Substituting $p = \frac{n-1}{n}$,we get $\frac{1}{(n-1)/n} = \frac{n}{9}$.This simplifies to $\frac{n}{n-1} = \frac{n}{9}$.Since $n > 1$,we can divide both sides by $n$ to get $\frac{1}{n-1} = \frac{1}{9}$.Therefore,$n - 1 = 9$,which implies $n = 10$.

$X$	$0$	$1$	$2$	$3$	$4$
$P(X)$	$0.1$	$0.5$	$0.2$	$-0.1$	$0.3$

$X$	$0$	$2$	$4$	$6$	$8$
$P(X)$	$a$	$2a$	$a+b$	$2b$	$3b$

$X = x$	$0$	$1$	$2$
$P(X = x)$	$4k - 10k^2$	$5k - 1$	$3k^3$

$A$ fair $n$ $(n > 1)$ faced die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$,then $n$ is equal to

Similar Questions

State which of the following is not a probability distribution of a random variable. Give reasons for your answer.

$X$ $0$ $1$ $2$ $3$ $4$

$P(X)$ $0.1$ $0.5$ $0.2$ $-0.1$ $0.3$

If the mean of the following probability distribution of a random variable $X$ is $\frac{46}{9}$,then the variance of the distribution is:

$X$ $0$ $2$ $4$ $6$ $8$

$P(X)$ $a$ $2a$ $a+b$ $2b$ $3b$

$A$ random variable $X$ has the following probability distribution:
$X = x$ $0$ $1$ $2$
$P(X = x)$ $4k - 10k^2$ $5k - 1$ $3k^3$

Then $P(X < 2)$ is:

If the mean of a Poisson distribution is $\frac{1}{3}$,then the ratio $P(X=1) : P(X=2)$ is

$A$ player tosses two coins. He wins $Rs. 1$ if $1$ head appears,$Rs. 2$ if $2$ heads appear. But he loses $Rs. 3$ if no head appears. The mean of the prize money is

Vedclass Test Series

Exam Paper Generator

Online Exam Module