Question

Expectation of the number on a die when thrown is

Answer 1

on a die there 1,2,3,4,5,6
so probability of 1 = 1/6
for 2= 1/6 and so on for 3 4 5 & 6
expectation = sum of X × p(X)
exp. = 1×1/6+2×2/6+3×1/6+4×1/6+5×1/6+6×1/6
exp. = {1+2+3+4+5+6}/6 = 21/6=3.5

Answer 2

$\frac{7}{2}$

A random variable's expectation, also known as its expected value, is a single figure that reveals a lot about the variable's behaviour. The expectation is roughly defined as the average value of the random variable, with each value weighted as per its probability.

Expectation= mean

Mean=average

Average=$\frac{sum of the numbers}{total number of items}$

On throwing the die, we will get 1,2,3,4,5,6

Sum of the numbers    = 1+2+3+4+5+6

                                     =21

Total number of items = 6

                      Average = 21/6

                                     = 7/2

Thus, the expectation is 7/2.