The p.m.f of a random variable X is P(X=x)=fr | vedclass

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

Question

(D) Given the p.m.f $P(X=x) = \frac{1}{32} \binom{5}{x}$ for $x \in \{0, 1, 2, 3, 4, 5\}$.$P(X \leq 2) = P(X=0) + P(X=1) + P(X=2)$$= \frac{1}{32} \lef

Vedclass · Accepted Answer

$P(X \leq 2) = P(X \geq 3)$

Vedclass · Answer

(D) Given the p.m.f $P(X=x) = \frac{1}{32} \binom{5}{x}$ for $x \in \{0, 1, 2, 3, 4, 5\}$.$P(X \leq 2) = P(X=0) + P(X=1) + P(X=2)$$= \frac{1}{32} \left[ \binom{5}{0} + \binom{5}{1} + \binom{5}{2} \right] = \frac{1}{32} (1 + 5 + 10) = \frac{16}{32} = \frac{1}{2}$.$P(X \geq 3) = P(X=3) + P(X=4) + P(X=5)$$= \frac{1}{32} \left[ \binom{5}{3} + \binom{5}{4} + \binom{5}{5} \right] = \frac{1}{32} (10 + 5 + 1) = \frac{16}{32} = \frac{1}{2}$.Since $P(X \leq 2) = \frac{1}{2}$ and $P(X \geq 3) = \frac{1}{2}$,it follows that $P(X \leq 2) = P(X \geq 3)$.

$X = x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(x)$	$k$	$2k$	$3k$	$4k$	$4k$	$3k$	$2k$	$k$	$k$

$X = x$	$-1.5$	$-0.5$	$0.5$	$1.5$	$2.5$
$P(X = x)$	$0.05$	$0.2$	$0.15$	$0.25$	$0.35$

The p.m.f of a random variable $X$ is $P(X=x)=\frac{1}{2^5}\binom{5}{x}$,where $x=0, 1, 2, 3, 4, 5$ and $P(X=x)=0$ otherwise. Then:

Similar Questions

$A$ random variable $X$ has the following probability distribution. Find the value of $k$ and the value of $P(3 < X \leq 6)$.
$X = x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$
$P(x)$ $k$ $2k$ $3k$ $4k$ $4k$ $3k$ $2k$ $k$ $k$

If $X$ is a random variable with cumulative distribution function $F(x)$ and its probability distribution is given by the following table:
$X = x$ $-1.5$ $-0.5$ $0.5$ $1.5$ $2.5$
$P(X = x)$ $0.05$ $0.2$ $0.15$ $0.25$ $0.35$

Then,find the value of $F(1.5) - F(-0.5)$.

$A$ random variable $X$ has its range $\{-1, 0, 1\}$. If its mean is $0.2$ and $P(X=0)=0.2$,then $P(X=1)=$

For a normal curve,the greatest ordinate is

From a well-shuffled pack of $52$ playing cards,cards are drawn one by one with replacement. The probability that the $5^{th}$ card will be the "king of hearts" is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module