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An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represent the number of black balls. What are the possible values of X? Is X a random variable?
Given: An urn containing 5 red and 2 black balls.
Let R represent red ball and B represent black ball.
Two balls are drawn randomly. Hence, the sample space of the experiment is S = {BB, BR, RB, RR}
X represents the number of black balls.
⇒ X(BB) = 2
X(BR) = 1
X(RB) = 1
X(RR) = 0
Therefore, X is a function on sample space whose range is {0, 1, 2}.
Thus, X is a random variable which can take the values 0, 1 or 2.
A random variable X has the following probability distribution:
X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
P(X) | 0 | k | 2k | 2k | 3k | K2 | 2 K2 | 7 K2 + k |
Determine
(i) k (ii) P(X < 3)
(iii) P(X > 6) (iv) P(0 < X < 3)