The probability distribution for a discrete random variable X is given below. The expectation value of X is (up to one decimal place)______.X 1 2 3 4 P(X) 0.3 0.4 0.2 0.1
Understanding Expectation Value Calculation
The expectation value, often denoted as E[X] or $\mu$, represents the weighted average of all possible values a discrete random variable can take. It's calculated by summing the product of each value and its corresponding probability.
Discrete Random Variable Probability Distribution
The provided probability distribution for the discrete random variable X is:
| X | 1 | 2 | 3 | 4 |
| P(X) | 0.3 | 0.4 | 0.2 | 0.1 |
Calculating the Expectation Value E[X]
The formula for the expectation value of a discrete random variable X is:
$ E[X] = \sum_{i} x_i P(X=x_i) $
Using the given distribution, we calculate the expectation value:
$ E[X] = (1 \times 0.3) + (2 \times 0.4) + (3 \times 0.2) + (4 \times 0.1) $
$ E[X] = 0.3 + 0.8 + 0.6 + 0.4 $
$ E[X] = 2.1 $
The expectation value of X, calculated to one decimal place, is 2.1.
Important Questions from Random Variables
If the odds in favour of any random event A are 5 ∶ 6, then the odds against the event are:
If random variable X follows binomial distribution with parameter n and p with mean 15 and variance 10, then the value of mode is
Let $X$ and $Y$ be continuous random variables with probability density functions $P_X(x)$ and $P_Y(y)$, respectively. Further, let $Y = X^2$ and $P_X(x) = \begin{cases} 1, & x\in (0,1] \\ 0, & \text{otherwise} \end{cases}$
Which one of the following options is correct?- Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable $X$ denote the sum of the outcomes obtained.
The expectation of $X$ is __________ (rounded off to two decimal places). - Let $X = aZ + b$, where $Z$ is a standard normal random variable, and $a, b$ are two unknown constants. It is given that
$E[X] = 1$, $E[(X – E[X])Z] = –2$, $E[(X – E[X])^2] = 4$,
where $E[X]$ denotes the expectation of random variable $X$. The values of $a, b$ are:
