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In Problems 9 and 10, graph f, and show that f satisfies the first two conditions for a probability density function.
10.
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- 3. Show that the following are probability density functions: 1 (a) f(x) = -2*, x = 1, 2, ..., N, and zero elsewhere 2N+1-2 (b) f(x)=p(1-p)*, x=0, 1, 2, ..., and zero elsewhere; 0arrow_forward2. The number of minutes a flight from Phoenix to Tucson is early or late is a random variable whose 1 (36– x*) for-6arrow_forward11. The distribution function of a random variable X is given by -e-x² X>0 otherwise F(x)= Find the probability density function.arrow_forward6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-oo, 00) is a function f such that f (x) >0 and | f (x) = 1. (a) Determine which of the following functions are probability density functions on the (-0, 00). x-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. xf(x) dr yields the expected value for a density f(x) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.arrow_forwardsolve only 4 and 5 plzarrow_forward7. If a random variable has the probability density function -1≤x≤3 otherwise f(x)=k(x²-1) =0arrow_forward5. Suppose that X is a continuous random variable whose probability density function is given by C(4x-2x2) 0 < x < 2 f(x) = otherwise What is the value of C?arrow_forwardV7arrow_forward. Find each probability.(a) X ∼ Gaussian (0, 3). Find P[X > 4.5].(b) Y ∼ Gaussian (50, 10). Find P[X < 75]arrow_forward6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-x, o0) is a function f such that f(r) 20 and (2) = = 1. (a) Determine which of the following functions are probability density functions on the (-x0, 00). fr-1 00 (b) We can also use probability density functions to find the erpected 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. rf(x) dr yields the expected value for a density f(r) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.arrow_forwardB- Show that if the following function be probability function: for 0arrow_forwardQ2. The probability density function of X is as follows. f(x) = 2 - 2x, for x = [0, 1] Which one of the following expressions can be used to find P(0.5 < X < 1.5)? F(x) is the cumulative distribution function of X. (A) 1 - F(0.5) (C) F (1.5)-f(0.5) (B) f(1.5)-f(0.5) (D) 1.5 (2 - 2x) dx (E) otherarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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