A person throws an unbiased die. If the numbe | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the random variable $X$ denote the gain or loss.When an unbiased die is thrown,the possible outcomes are $\{1, 2, 3, 4, 5, 6\}$,each with a pr

Vedclass · Accepted Answer

$0.5$

Vedclass · Answer

(D) Let the random variable $X$ denote the gain or loss.When an unbiased die is thrown,the possible outcomes are $\{1, 2, 3, 4, 5, 6\}$,each with a probability of $\frac{1}{6}$.If the number is even,the gain is equal to the number shown $(X = x)$.If the number is odd,the loss is equal to the number shown $(X = -x)$.The probability distribution of $X$ is:$X = x$$-1$$2$$-3$$4$$-5$$6$$P(X = x)$$\frac{1}{6}$$\frac{1}{6}$$\frac{1}{6}$$\frac{1}{6}$$\frac{1}{6}$$\frac{1}{6}$The expectation $E(X)$ is given by $\sum x \cdot P(X=x)$:$E(X) = (-1) \cdot \frac{1}{6} + 2 \cdot \frac{1}{6} + (-3) \cdot \frac{1}{6} + 4 \cdot \frac{1}{6} + (-5) \cdot \frac{1}{6} + 6 \cdot \frac{1}{6}$$E(X) = \frac{-1 + 2 - 3 + 4 - 5 + 6}{6}$$E(X) = \frac{3}{6} = 0.5$Thus,the expectation is ₹ $0.5$.

$X = x_i$	$0$	$1$	$2$	$3$
$P(X = x_i)$	$k$	$3k$	$3k$	$k$

$A$ person throws an unbiased die. If the number shown is even,he gains an amount equal to the number shown. If the number is odd,he loses an amount equal to the number shown. Then his expectation is ₹.

Similar Questions

If $X$ is a random variable with the distribution given below:
$X = x_i$ $0$ $1$ $2$ $3$
$P(X = x_i)$ $k$ $3k$ $3k$ $k$

Then the value of $k$ and its variance are respectively given by:

$A$ person draws a card from a pack of $52$ cards and replaces it. After shuffling,he draws a card again. If he repeats this process,what is the probability that he draws a red card for the first time on the third draw?

If $X$ is a Poisson variable such that $3 P(X=4)=\frac{1}{2} P(X=2)+P(X=0)$,then the mean of $X$ is

An unbiased coin is tossed $5$ times. Suppose that a variable $X$ is assigned the value $k$ when $k$ consecutive heads are obtained for $k=3, 4, 5$; otherwise,$X$ takes the value $-1$. Then the expected value of $X$ is:

In a game,$3$ coins are tossed. $A$ person is paid ₹ $7$ if he gets all heads or all tails,and he is supposed to pay ₹ $3$ if he gets one head or two heads. The amount he can expect to win on an average per game is ₹

Vedclass Test Series

Exam Paper Generator

Online Exam Module