Exercise · ZW-PROBABILITY-MASS-FUNCTION-003 · ★☆☆ Basic
Which of these tables can be the probability mass function of a variable with values 1, 2 and 3 (probabilities of \(x=1,2,3\))?
Choose one option.
Show answer
- B. 0.5, 0.3, 0.2
Explanation
The masses must be non-negative and add up to 1. Only 0.5+0.3+0.2=1; the others add up to 1.2, 1 with a negative value, and 0.6.
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-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-007 Which statement about a probability mass function is correct?
- 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.
← ZW-PROBABILITY-MASS-FUNCTION-002 ZW-PROBABILITY-MASS-FUNCTION-004 →