If the probability distribution of a random variable $\mathrm{X}$ is as given below: $\begin{array}{*{20}{c}} {X = x:}&{ - 2}&{ - 1}&0&1&2&3 \\ {P(X = x):}&{\frac{1}{{10}}}&k&{\frac{1}{5}}&{2k}&{\frac{3}{{10}}}&k \end{array}$ Then the value of $k$, is

JEE MATHEMATICS MCQ: PROBABILITY

1 Easy

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Application +4 | -1

If the probability distribution of a random variable

\mathrm{X}

is as given below:

\begin{array}{cccccccccccccccccccc} {X = x:}&{ - 2}&{ - 1}&0&1&2&3 \\ {P(X = x):}&{\frac{1}{{10}}}&k&{\frac{1}{5}}&{2k}&{\frac{3}{{10}}}&k \end{array}

Then the value of

k

, is

View answer and explanation

Correct option: A

\frac{1}{10}

Option A (

\frac{1}{10}

) is correct because the sum of probabilities in a probability distribution must equal 1, allowing us to solve for k.

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\begin{array}{cccccc}X: & 1 & 2 & 3 & 4 & 5 \\ P(X): & k^2 & 2 k & k & 2 k & 5 k^2\end{array}

P(X>2)

\left( {2\;n + 1} \right)

n

n + 1

n

A

B

P\left( {A \cap B'} \right) = \frac{3}{{25}}

P\left( {A' \cap B} \right) = \frac{8}{{25}}

P\left( A \right)

A

B

A

B

B

A