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.Suppose you have the probability density function a² if 1< < 7 114 f(x) = otherwise Find the cumulative distribution function of X. if Select an answer v F(x) = if Select an answer v if Select an answer ♥Suppose you have the probability density function if 3 < x < 9 f(x) otherwise Find the cumulative distribution function of X. Select an answer ♥ F(x) if Select an answer if Select an answer Note: When writing your piecewise function, start with the left-most interval.
- 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).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.
- 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.Please do these 3 Qs in excel or show steps, thank you. Do not randomly write wrong answer if don't know how to solve
- For a particular kind of battery, the probability density function for x hours to be the life of a battery selected at random is given by -x/60 x > 0 f(x) = - 60 0, x < 0 Find the probability that the life of a battery selected at random will be between 15 and 25 hours.please quickly thanks !A cube with 35-cm-long sides is sitting on the bottom of an aquarium in which the water is one meter deep. (Round your answers to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.) (a) Estimate the hydrostatic force on the top of the cube. (b) Estimate the hydrostatic force on one of the sides of the cube. N
