Exercise · ZW-PROBABILITY-MASS-FUNCTION-007 · ★★☆ Intermediate
Which statement about a probability mass function is correct?
Choose one option.
Show answer
- A. Each mass is between 0 and 1 and all of them add up to 1
Explanation
The masses are probabilities (between 0 and 1) and, since they cover all possible values, add up to 1. They need not be equal.
Review the concept: Probability mass function
The probability mass function \(p_X\) of a discrete random variable \(X\) gives, for each value \(x\) it can take, the probability \(P\) that it takes it.
\[p_X(x)=P(X=x)\]
More practice problems: probability mass function
- ZW-PROBABILITY-MASS-FUNCTION-001 A variable X takes the values 0, 1 and 2 with p(0)=0.2, p(1)=c and p(2)=0.5. What is c?
- ZW-PROBABILITY-MASS-FUNCTION-002 With two dice, X is the sum. What is p_X(7)?
- ZW-PROBABILITY-MASS-FUNCTION-003 Which of these tables can be the probability mass function of a variable with values 1, 2 and 3 (pr…
- ZW-PROBABILITY-MASS-FUNCTION-004 Let p(x)=kx for x=1,2,3,4 and 0 otherwise. What value must k have?
- ZW-PROBABILITY-MASS-FUNCTION-005 With p(x)=tfracx10 for x=1,2,3,4, compute P(X≥3).
- ZW-PROBABILITY-MASS-FUNCTION-006 Three fair coins are tossed and X is the number of heads. Compute p_X(2).
- ZW-PROBABILITY-MASS-FUNCTION-008 X takes the values 0, 1, 2, 3 with masses 0.1, 0.3, 0.4, 0.2. Compute P(1≤ X≤ 2).
- ZW-PROBABILITY-MASS-FUNCTION-009 Let p(x)=(tfrac12)^x for x=1,2,3,dots. Compute the probability that X is even.
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