If a probability density function for X is f(x) define F(x) over the whole real line. = 2(x+1)² for 0 < x < 2, find F(x). Make sure you
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- Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.Let X be the number of years before a particular type of machines will need replacement. Assume that X has the probability function f(1) = 0.1, f(2) = 0.2, f(3) = 0.2, f(4) = 0.2, f(5) = 0.3. Find the probability that the machine needs no replacement during the first 3 years.Solve for R. Show all work.
- The probability density function of X, the lifetime of a certain type of device (measured in months), is given by 0 if\a 16 f(z) = Find the following: P(X > 23) = The cumulative distribution function of X: If r 16 then F(x)= The probability that at least one out of 7 devices of this type will function for at least 35 months:Tossa coin once, S = (H,T) with P,(H) = p and P,(T) = q. Define X(-) by X(H) = ₁ X(T) = 0. Compute and plot the probability distribution function F, (x).Which statements below are true for a probability distribution function (pdf), f(x)? The total area under f(x) is equal to 1. f(x) is non-decreasing f(x) is a probability f(x) is non-negative x is non-negative
- Let f(x) = k(4x –x²) if 03. (a) For what value of k is f(x) a probability density function? (b) For that value of k, find P (x>2). (c) Find the mean.please use the pictures below.Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-∞,0) is a function f such that f(2) 20 and Lsla) = 1. (a) Determine which of the following functions are probability density functions on the (-00, 00). (1-1 00 (b) We can also use probability density functions to find the expected value of the outcomes of the event - if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. zf(z) dz yields the expected value for a density f(x) with domain on the real mumbers.) Find the expected value for one of the valid probability densities above.
- 10) Let f(x) by the probability density function of some continuous random variable. Explain why it must be true that f(x) dx =1.f(x), a continuous probability function, is equal to 1/12, and the function is restricted to 0Find the value of c so that the function f(x) below is a valid probability density function. f(x)={c(x2+x)0if 0≤x≤1,otherwise.SEE MORE QUESTIONS
