Suppose that X follows a poisson distribution with parameter λ=1.416 . P(X≥0)≅?

Suppose that the lifetime in years, X,  of a type of electrical switch follows the distribution f(x)=12e−x2f(x)=12e−x2for x>0x>0. What type of continuous distribution is this and what is the average lifetime of one of these switches?

3.2.5. Let X have a Poisson distribution with u = 100. Use Chebyshev's inequality to determine a lower bound for P(75 < X < 125). Next, calculate the probability

Its x-12.5 not expone

Suppose that you enter a fantasy basketball league. Suppose that the 2022 team budget, say X, is randomly drawn from a uniform distribution on the interval [90, 210], where the unit is U.S. million dollars. In addition, suppose that after the value X = x has been observed (90 < x < 210), the 2023 team budget, say Y, is randomly drawn from a uniform distribution on the interval [x, 210]. In other words, the 2023 budget is at least as large as the 2022 budget. (a) For any given value of x (90 < x < 210), obtain E[Y|X = x]. (b) In view of part (i), obtain E[Y|X]. (c) What is the difference between E[Y|X = x] and E[Y|X]? (d) Obtain E[Y]. That is, what is the expected value of your 2023 fantasy basketball budget? (e) Golden State Warriors won the 2022 NBA finals. Their estimated 2022 payroll is about $194 million. Would your 2023 fantasy basketball budget be on average larger than Golden State Warriors' 2022 payroll? Explain briefly.

If a random variable X ∼ Exponential(1). Find the distribution of Y = X/λ.

Use the geometric distribution to derive E(Y), E(Y^2), and V(Y) from the Poisson distribution

If F(x) is the cumulative distribution function (CDF) for X ~ Poisson (1.6), find the following values: a) F(0) b) F(1.2) c) F(2) c) F(-4.5)

part d please

Find P(11<X<15) If X is normally distributed with a mean of 14 and a standard deviation of 2?