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In Problems 25 and 26, graph f, and show that f satisfies the first two conditions for a probability density function.
26.
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Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
- Show that each function defined as follows is a probability density function on the given interval; then the indicated probabilities. f(x)=12(1+x)3/2;[0,) a. P(0X2) b. P(1X3) c. P(X5)arrow_forwardShow that each function defined as follows is a probability density function on the given interval; then find the indicated probabilities. f(x)=(1/2)ex/2;[0,) a. P(0X1) b. P(1X3) c. P(X2)arrow_forward4. Show the following function is a legitimate probability mass function. Px(x) = Pr(X = x) = ())*(** " x = 0, 1, 2,..., n.arrow_forward
- 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_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 (-0, 0) is a function f such that f(r) > 0 and (2) = 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. rf(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_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_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_forwardConsider the three functions I. f(x)= {1-x if 0 < x < 2 {0 otherwise II. f(x)= {1+x if 0 < x < 2 {0 otherwise III. f(x)= {(3/27)x^2) if 0< x < 3) {0 otherwise Which of these above functions can be probability distributions? And why?arrow_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_forward3. If a random variable has the probability density |2e-2* f (x) = - for x >0 for x <0 Find the probability that it will take on a value between 0.5 and 1.arrow_forward27. If the probability density function of X is 322 0 < * < a s(z) = { a 0, otherwise. then E(X)is 3 A. В. С. D. B. ereviarrow_forwardarrow_back_iosarrow_forward_iosRecommended textbooks for you
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