Find the mean of the sum of points on 2 unbiased dice

(i) find the variance of the number obtained on a throw of an unbaised die (ii) what is the mathematical expectation of the sum of points on n dice ?

Let E denote the random experimnet of rolling two unbiased dice and A and B are two events connected with E. The event A occur if the sum of the digits shown on the two dice is 7 while the event B occurs if at least one of the dice shows up a 4. show that the events A and B neither mutually exclusive nor exhaustive.

Find the sum of the focal distances of any point on the ellipse 9x^2+16 y^2=144.

Find the sum of the focal distance of any point on the ellipse 9x^(2) +25y^(2) = 225 .

Let X be the random variable of the number of points obtained in single throw of an unbiased die. Then, the value of barX is -

The arithmetic mean of the marks obtained in 8 different subjects in a school are given below. Find the average of the sum of the marks of 8 subjects.

Find the sample space of the random experiment of throwing an unbiased die until a 1 turns up.

Two dice are thrown simultaneously. What is the probability that the sum of the points on the two dice is 5?

Given that the two numbers appearing on throwing two dice are different. Find the probability of the event the sum of numbers on the dice is 4".

Two dice are thrown and the sum of the number which come up on the dice is noted. Let us consider the following events associated with the experiment A: 'the sum is even'. B: 'the sum is a multiple of 3'. C: 'the sum is less than 4'. D: 'the sum is greater than 11'. Which pairs of these events are mutually exclusive?