suppose x is a uniform random variable with c=40 ana d= 70 find the probability that a randomly selected observation is between 43 and 65

To find the probability that a randomly selected observation from a uniform random variable is between 43 and 65, we need to calculate the area under the probability density function (PDF) curve between those two values.

The PDF of a uniform random variable is a constant function over its support interval. In this case, the support interval is [40, 70], which means that x can take any value between 40 and 70, inclusive, with equal probability.

To calculate the probability between 43 and 65, we need to find the proportion of the total interval [40, 70] that falls within [43, 65]. This can be done by dividing the width of the subinterval [43, 65] by the width of the entire interval [40, 70].

Width of [43, 65] = 65 - 43 = 22
Width of [40, 70] = 70 - 40 = 30

Therefore, the probability that a randomly selected observation is between 43 and 65 is:

Probability = Width of [43, 65] / Width of [40, 70]
= 22 / 30
= 0.7333 (rounded to 4 decimal places)

So, the probability is approximately 0.7333 or 73.33%.