Final answer:
To find the probability between 20 and 35, calculate the area under the probability density function. The expectation is 50 and the variance is 833.33.
Step-by-step explanation:
To find the probability that the value of the random variable is between 20 and 35, we need to calculate the area under the probability density function curve within that interval. Since the distribution is uniform, the probability density function is a rectangle with base 100 and height 1/100. The area of the rectangle between 20 and 35 is then (35-20)*(1/100) = 15/100 = 0.15.
To determine the expectation of the random variable, we use the formula E(X) = (a+b)/2, where a and b are the endpoints of the interval. In this case, a = 0 and b = 100. Therefore, E(X) = (0+100)/2 = 50. For the variance, we use the formula Var(X) = (b-a)^2/12. Plugging in the values, we get Var(X) = (100-0)^2/12 = 10000/12 = 833.33.