Question

Suppose a continuous random variable X is uniformly distributed on the interval (i) [0, 10]; (ii) [-3, 6]. Find a number k so that P(1 ≤ x ≤ k) = 0.3.

Answer 1

To find a number k such that P(1 ≤ x ≤ k) = 0.3 for a continuous random variable X that is uniformly distributed on the interval [0, 10], we need to find the corresponding area under the probability density function. The area is determined by the length of the interval and the probability density function value. In this case, the value of k is 4.

Step-by-step explanation:

To find a number k such that P(1 ≤ x ≤ k) = 0.3 for a continuous random variable X that is uniformly distributed on the interval [0, 10], we need to find the corresponding area under the probability density function.

Since the distribution is a uniform distribution, the probability density function is a constant value over the interval. In this case, the constant value is 1/10 because the interval is of length 10.

The area under the probability density function from 1 to k is given by (k - 1) * (1/10), and this should be equal to 0.3.

(k - 1) * (1/10) = 0.3

Simplifying this equation, we get k - 1 = 3, which gives us k = 4.