Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.
Given: A die is thrown two times.
When a die is tossed two times then the number of observations will be (6 × 6) = 36.
Now, let X is a random variable which represents the success and is given as six appears on at least one die.
P(X = 0) = P(six does not appear on any of die)
P(X = 1) = P(six appears atleast once of the die)
P(X = 2) = P(six does appear on both of die)
Hence, the required probability distribution is,
Therefore Expectation of X E(X):
7 K2 + k
(i) k (ii) P(X < 3)
(iii) P(X > 6) (iv) P(0 < X < 3)
A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and standard deviation of X.