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QJEEM21Maa193: JEE Main 2021 Mathematics - Class 12 JEEM21Maa193 Solution: The probability distribution of random variable X is given by : …

The probability distribution of random variable X is given by :

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


Let p = P(1 < X < 4 | X < 3). If 5p = λ\lambda K, then λ\lambda equal to ___________.

Step-by-Step Verified Solution

∑P(X)=1⇒k+2k+3k+k=1\sum {P(X) = 1 \Rightarrow k + 2k + 3} k + k = 1

⇒k=19\Rightarrow k = {1 \over 9}

Now, p = P\left( {{{kx &lt; 4} \over {X &lt; 3}}} \right) = {{P(X = 2)} \over {P(X &lt; 3)}} = {{{{2k} \over {9k}}} \over {{k \over {9k}} + {{2k} \over {9k}}}} = {2 \over 3}

⇒p=23\Rightarrow p = {2 \over 3}

Now, 5p=λk5p = \lambda k

⇒(5)(23)=λ(1/9)\Rightarrow (5)\left( {{2 \over 3}} \right) = \lambda (1/9)

⇒λ=30\Rightarrow \lambda = 30

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