Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

Find the expected value of the number on a die when thrown.

Can you answer this question?

1 Answer

0 votes
  • If S is a sample space with a probability measure and X is a real valued function defined over the elements of S, then X is called a random variable.
  • Types of Random variables :
  • (1) Discrete Random variable (2) Continuous Random variable
  • Discrete Random Variable :If a random variable takes only a finite or a countable number of values, it is called a discrete random variable.
  • Continuous Random Variable :A Random Variable X is said to be continuous if it can take all possible values between certain given limits. i.e., X is said to be continuous if its values cannot be put in 1 − 1 correspondence with N, the set of Natural numbers.
  • The probability mass function (a discrete probability function) $P(x)$ is a function that satisfies the following properties :
  • (1) $P(X=x)=P(x)=P_x$
  • (2) $P(x)\geq 0$ for all real $x$
  • (3) $\sum P_i=1$
  • Moments of a discrete random variable :
  • (i) About the origin : $\mu_r'=E(X^r)=\sum P_ix_i^{\Large r}$
  • First moment : $\mu_1'=E(X)=\sum P_ix_i$
  • Second moment : $\mu_2'=E(X^2)=\sum P_ix_i^2$
  • (ii) About the mean : $\mu_n=E(X-\bar{X})^n=\sum (x_i-\bar{x})^nP_i$
  • First moment : $\mu_1=0$
  • Second moment : $\mu_2=E(X-\bar{X})^2=E(X^2)-[E(X)]^2=\mu_2'-(\mu_1')^2$
  • $\mu_2=Var(X)$
Step 1:
Let $X$ be the random variable denoting the number that turns up when a die is thrown.
$X$ takes the values 1,2,3,4,5,6
Step 2:
Now each of these values is equally likely $P(x_i)=\large\frac{1}{6}$$(i=1,2,......6)$
Step 3:
The probability of $X$ is given by
Step 4:
$E(X)=\sum P_i x_i=1\times \large\frac{1}{6}$$+2\times \large\frac{1}{6}$$+3\times \large\frac{1}{6}$$+4\times \large\frac{1}{6}$$+5\times \large\frac{1}{6}$$+6\times \large\frac{1}{6}$
$\Rightarrow \large\frac{1}{6}$$\times 21=\large\frac{7}{2}$$=3.5$
answered Sep 17, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App