Let X be a discrete random variable with the following PMFfor x=oPX(x) = for x=1for x=20 otherwise(a) Find RX, the range of the random variable X.(b) Find P(X ≥ 1.5).(c) Find P(0 < X < 2).(d) Find P(X = 0|X < 2)

It seems like there's some information missing from your question, specifically the probabilities for when x=0, x=1, and x=2. However, I can still explain how to approach these problems.

(a) The range of a random variable X, denoted as RX, is the set of all possible outcomes or values that X can take. In this case, based on the provided PMF, the range RX of the random variable X is {0, 1, 2}.

(b) P(X ≥ 1.5) is the probability that the random variable X takes on a value greater than or equal to 1.5. Since X is a discrete random variable and can only take on the values 0, 1, 2, the only value in its range that is greater than or equal to 1.5 is 2. So, P(X ≥ 1.5) is the same as P(X = 2), which you can find from the given PMF.

(c) P(0 < X < 2) is the probability that X takes on a value between 0 and 2, exclusive. The only value in the range of X that satisfies this condition is 1. So, P(0 < X < 2) is the same as P(X = 1), which you can find from the given PMF.

(d) P(X = 0|X < 2) is the conditional probability that X equals 0 given that X is less than 2. Since the only values X can take on that are less than 2 are 0 and 1, this probability is P(X = 0) divided by P(X = 0) + P(X = 1), which you can find from the given PMF.

It seems like there's some information missing from your question, specifically the probabilities for when x=0, x=1, and x=2. However, I can still explain how to approach these problems.

(a) The range of a random variable X, denoted as RX, is the set of all possible outcomes or values that X can take. In this case, based on the given PMF, the range RX of the random variable X is {0, 1, 2}.

(b) P(X ≥ 1.5) is the probability that the random variable X takes on a value greater than or equal to 1.5. Since X is a discrete random variable and can only take on the values 0, 1, 2, the only value in its range that is greater than or equal to 1.5 is 2. So, P(X ≥ 1.5) is the same as P(X = 2), which is given in the PMF.

(c) P(0 < X < 2) is the probability that X takes on a value between 0 and 2, exclusive. The only value in the range of X that satisfies this condition is 1. So, P(0 < X < 2) is the same as P(X = 1), which is given in the PMF.

(d) P(X = 0|X < 2) is the conditional probability that X equals 0 given that X is less than 2. Since the only values X can take on that are less than 2 are 0 and 1, this probability is P(X = 0) divided by P(X = 0) + P(X = 1), which can be calculated using the given PMF.

Please provide the specific probabilities for when x=0, x=1, and x=2 so I can give a more accurate answer.