In a nickel-cadmium battery NiCd, a fully charged cell consists of nickelic hydroxide. Nickel is an element which has multiple oxidation states. Let X be the charge of nickel, which has the following probability mass function: 1| fx(x) 0.18 1 0.34 0.33 4 0.15 Determine the mean charge of nickel. A. 2.0 B. 1.5 C. 1.6 D. 1.45 E. none of the preceding

Consider the following set of five independent measurements of some unknown random quantity: -1.5, 0.3, -1.2, -0.2, 0.5. Based on these measurements, we can estimate E(X)=?  (accurate to at least four decimal places). Based on these measurements, we can estimate Var(X)=? (accurate to at least four decimal places).

The probability mass function of the r.v.x is : -2 3 f(x) = P(X=x) 0.15 0.45 0.3 0.10 %3D The expected value E(x) is O A. 0.15 ОВ. 1.05 OC. 1.2 O D.0.45

This is a Statistics problem. Please explain each step thoroughly. The problem I'm having issues with is shown below:

Chapters: Normal and Exponential random variables. Q: Let X be an exponential random variable with rate 1. If a and b are positive numbers, then P(X > a + b|X > b) = P(X > a). a. Explain why this is called the memoryless property b. Show that for an exponential rv X with rate 1, P(X > a) = e-ad.

Below is the life table of a population of waterbuck. What is the probability that an individual in stage 2 will survive to stage 3 (give your answer to three decimal places)? Stage 0 1 2 3 4 5 ax 50 39 25 20 11 4 Answer: 0.200 1.00 0.78 0.50 0.40 0.22 0.08 Ix dx 11 14 5 9 7 4 Probability of survival = lx+1/lx The correct answer is: 0.8 0.220 0.359 0.200 0.450 0.636 1.000 qx X

Let A and B be independent exponential random variables, both with mean 1. If U = A + B and V = A/B, find the joint pdf of U and V.