An infrastructure project calls for investment in 2021. A team of experts has reached a conclusion that the probability that the project is going to fail follows a continuous uniform distribution between 0.3 and 0.7. What is the probability that the probability of project failure is between 0.2 and 0.5?  Group of answer choices0.250.20.50.75

Suppose that the random variable X is continuous and takes its values uniformly over the interval from 0 to 2. What is the value of the probability P{X ≤ 0.4 or X > 1.2}?

The probability distribution for the number of defects during an 8-hour shift on the assembly line at Wanda’s Wooden Widgets is as shown in the chart below.x 0 1 2 3 4 5P(X = x) 0.50 0.25 0.15 0.06 0.03 0.01What is the probability that in a given shift there will be at most 2 defects? 0.90 0.75 0.40 0.10 1.00

Uniform DistributionWhat is the probability of the random variable X lying between -1.5 and +2.5, i.e. P(-1.5<X<2.5)?

In a certain manufacturing process, 5% of the tools produced turn out to bedefective. Find the probability that in a sample of 40 tools, at most 2 will bedefective: [Given: e-2 = 0.135](a) 0.555(b) 0.932(c) 0.785(d) 0.675

1. A property development company takes on one new project each year, investing all of its capital in that year’sproject. If the project is successful, the company makes a profit of $1million. If the project is unsuccessful,the company is ruined (loses all its money) and ceases to exist. The success or failure of each project isindependent of all previous ones. The probability that a project is unsuccessful when x million dollars isinvested (for x = 1, 2, 3, . . .) is 1/(x + 1) 2 . Let X n million dollars be the company’s total capital after nprojects.(a) Write down the transition probabilities for the Markov chain (X n ).(b) Show that when X 0 = i, the probability h i of eventual ruin is 1i+1