In a particular discrete probability distribution the random variable X takes the value 120/r with probability r/45,

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In a particular discrete probability distribution the random variable X takes the value 120/r with probability r/45, where r takes all integer values from 1 to 9 inclusive.

i. Show that P(X = 40) = 1/15.

ii. Construct the probability distribution table for X.

iii. Which is the modal value of X?

iv. Find the probability that X lies between 18 and 100.

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