Question

1. a random variable x has a probability distribution as follows:

x	p(x)
1	2k
2	5k
3	3k
4	4k

what is p(x < 2)?
a) 1/17
b) 5/17
c) 10/17
d) 13/17
e) cannot be determined.

Explanation:

Step1: Recall probability - sum property

The sum of all probabilities in a probability distribution is 1. So, \(3k + 2k+5k + 3k+4k=1\).

Step2: Combine like - terms

\((3 + 2+5 + 3+4)k=1\), which simplifies to \(17k = 1\), and then \(k=\frac{1}{17}\).

Step3: Find \(P(X < 2)\)

\(P(X < 2)=P(X = 0)+P(X = 1)\). Since \(P(X = 0)=3k\) and \(P(X = 1)=2k\), then \(P(X < 2)=3k + 2k=5k\).

Step4: Substitute \(k\) value

Substitute \(k = \frac{1}{17}\) into \(5k\), we get \(P(X < 2)=\frac{5}{17}\).

Answer:

B. 5/17