Question

suppose x is a uniform random variable with c = 30 and d = 50. find p(x = 42).

0.4
0.6
0.1
0

Explanation:

Identify the distribution type

The problem states that \(x\) is a uniform random variable with parameters \(c = 30\) and \(d = 50\). This represents a continuous uniform distribution over the interval \([30, 50]\).

Recall continuous probability properties

For any continuous random variable, the probability of the variable taking on any exact single value is always zero. This is because the area under the probability density function curve at a single point is zero.

Calculate the probability

We want to find \(P(x = 42)\). Since \(x\) is a continuous random variable:

$$ P(x = 42) = 0 $$

Match with the options

The calculated probability is \(0\), which corresponds to the fourth option.

Answer:

• 0.4
• 0.6
• 0.1
• 0 (Correct answer)