For the following probability distribution of a random variable $X$, the Expected value and Variance of $X$ are respectively
$X = x$ $1$ $2$ $3$
$P(X = x)$ $1/5$ $2/5$ $2/5$

Question

The integral $ \int e^x \frac{2 + \sin 2x}{1 + \cos 2x} \, dx $ is equal to

Answer 1

Step 1: Approach
Use the definition of variance as the average squared deviation from the mean.

Step 2: Mean
$\mu=\dfrac{11}{5}=2.2$.

Step 3: Deviations
$(1-2.2)^2=1.44$, $(2-2.2)^2=0.04$, $(3-2.2)^2=0.64$.

Step 4: Weighted average
$\sigma^2=0.2(1.44)+0.4(0.04)+0.4(0.64)=0.288+0.016+0.256=0.56=\dfrac{14}{25}$.

Step 5: Answer
Option (B).

Final Answer:
The mean is 11/5 and the variance is 14/25, option (B). \[ \boxed{\frac{11}{5},\ \frac{14}{25}} \]

\(X = x\)	\(1\)	\(2\)	\(3\)
\(P(X = x)\)	\(1/5\)	\(2/5\)	\(2/5\)

x	0	1	2	3	4
P(x)	k	2k	4k	6k	8k

For the following probability distribution of a random variable \(X\), the Expected value and Variance of \(X\) are respectively
\(X = x\) \(1\) \(2\) \(3\)
\(P(X = x)\) \(1/5\) \(2/5\) \(2/5\)

Show Hint

The Correct Option is B

Solution and Explanation

Top Questions on Random Variables

Questions Asked in MHT CET exam

For the following probability distribution of a random variable \(X\), the Expected value and Variance of \(X\) are respectively\(X = x\)\(1\)\(2\)\(3\)\(P(X = x)\)\(1/5\)\(2/5\)\(2/5\)