The probability distribution of random variable X is given by: X 1 2 3 4 5 P ( X ) K 2 K 2 K 3 K K Let p = P ( 1 < X < 4 ∣ X < 3 ) . If 5 p = λ K , then λ is equal to

Σ P ( X ) = 1 ⇒ K + 2 K + 2 K + 3 K + K = 1 K = 1 9 P = P ( 1 < X < 4 ∣ X < 3 ) = P ( X = 2 ) P ( X < 3 ) P = 2 K 9 K K 9 K + 2 k 9 K = 2 3 5 P = λ K 5 × 2 3 = λ × 1 9 ⇒ λ = 30

Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityRandom Variable and its Probability DistributionEasy2 minPYQ_2021

MathematicsEasynumerical

The probability distribution of random variable $X$ is given by:

$X$	$1$	$2$	$3$	$4$	$5$
$P (X)$	$K$	$2 K$	$2 K$	$3 K$	$K$

Let $p = P (1 < X < 4 ∣ X < 3)$ . If $5 p = λ K$ , then $λ$ is equal to

Answer:

30.00

Solution:

$Σ P (X) = 1$
$\Rightarrow K + 2 K + 2 K + 3 K + K = 1$
$K = \frac{1}{9}$
$P = P (1 < X < 4 ∣ X < 3) = \frac{P (X = 2)}{P (X < 3)}$
$P = \frac{\frac{2 K}{9 K}}{\frac{K}{9 K} + \frac{2 k}{9 K}} = \frac{2}{3}$
$5 P = λ K$
$5 \times \frac{2}{3} = λ \times \frac{1}{9} \Rightarrow λ = 30$

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:Random Variable and its Probability Distribution

⏱ 2mℹ️ Source: PYQ_2021

Doubts & Discussion

Loading discussions...