Let pX(x)=x / 15, x=1,2,3,4,5, zero elsewhere, be the pmf of X. Find P(X=1 or 2), P((1)/(2)<X<(5

step 1 Problem 3, the probability mass function for the random variable xBX of x equals x divided by 15

Let pX(x)=x / 15, x=1,2,3,4,5, zero elsewhere, be the pmf of...

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Key Concepts

Probability of Inequality Events

Inequality events involve conditions such as 'less than', 'greater than', or 'between' among discrete outcomes. To calculate the probability of such events, one identifies all the discrete values that satisfy the inequality and sums their corresponding probabilities from the probability mass function.

Probability Mass Function (pmf)

A probability mass function defines the probability that a discrete random variable takes on each of its possible values. It assigns a non-negative probability to each value in the variable's support, with the condition that the sum of all probabilities equals one. This concept is crucial in understanding random variables defined over countable outcomes.

Discrete Random Variable

A discrete random variable is one that can take a countable number of distinct values, such as specific integers. Its behavior is fully described by its probability mass function, and probabilities of various events are computed by summing the pmf over the relevant set of outcomes.

Summation of Probabilities for Events

When calculating the probability of an event for a discrete random variable, the total probability is found by summing the probabilities of all individual outcomes that satisfy the event's conditions. This process is essential for combining probabilities of non-overlapping outcomes.

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