The range of a discrete random variable X is | vedclass

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

Question

(A) For a discrete random variable, the sum of all probabilities must be equal to $1$. Therefore, $P(X=1) + P(X=2) + P(X=3) = 1$. Substituting the giv

Vedclass · Accepted Answer

$\frac{2}{3}$

Vedclass · Answer

(A) For a discrete random variable, the sum of all probabilities must be equal to $1$. Therefore, $P(X=1) + P(X=2) + P(X=3) = 1$. Substituting the given values: $3k^3 + 2k^2 + (7 - 19k) = 1$. $3k^3 + 2k^2 - 19k + 6 = 0$. By testing values, if $k = 3$, $3(27) + 2(9) - 19(3) + 6 = 81 + 18 - 57 + 6 = 48 
eq 0$. If $k = \frac{1}{3}$, $3(\frac{1}{27}) + 2(\frac{1}{9}) - 19(\frac{1}{3}) + 6 = \frac{1}{9} + \frac{2}{9} - \frac{57}{9} + \frac{54}{9} = 0$. So, $k = \frac{1}{3}$ is a root. Now, $P(X=3) = 7 - 19k = 7 - 19(\frac{1}{3}) = 7 - \frac{19}{3} = \frac{21 - 19}{3} = \frac{2}{3}$.

The range of a discrete random variable $X$ is $\{1, 2, 3\}$ and the probabilities of its elements are given by $P(X=1) = 3k^3$, $P(X=2) = 2k^2$, and $P(X=3) = 7 - 19k$. Then $P(X=3) = $

Similar Questions

$A$ fair six-faced die is rolled $12$ times. The probability that each face turns up exactly twice is equal to:

If the function $P[X = x] = \begin{cases} \frac{K \cdot 2^x}{x!}, & x = 0, 1, 2, 3 \\ 0, & \text{otherwise} \end{cases}$ forms a probability mass function (p.m.f.),then the value of $K$ is:

$A$ person who tosses an unbiased coin gains two points for turning up a head and loses one point for a tail. If three coins are tossed and the total score $X$ is observed, then the range of $X$ is

Find the probability distribution of the number of successes in two tosses of a die,where a success is defined as a number greater than $4$.

If $X$ is a Poisson variate with $P(X=0)=0.8$, then the variance of $X$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module