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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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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_forward5. Prove or refute the following: If f(x) and f(x) are two probability density functions, then a f(x) + (1-a) f₂(x), 0≤a ≤ 1, is also a probability density functionarrow_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_forward20. Most computer languages have a function that can be used to generate random numbers. In Microsoft's Excel, the RAND function can be used to generate random numbers be- tween 0 and 1. If we let x denote the random number generated, then x is a continuous random variable with the probability density function: a. f(x) = Graph the probability density function. for 0 ≤ x ≤1 elsewherearrow_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_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_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_forward1. Suppose that for a certain life the probability density function is fx (x) ; 1+x Find () the survival function of x (i) the probability that the life aged 25 will die within next 15 years. (i) the probability that the life aged 42 will die between 55 and 62.arrow_forward7. If a random variable has the probability density function -1≤x≤3 otherwise f(x)=k(x²-1) =0arrow_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_forward7. )The cumulative distribution function of a random variable X is defined by the equation if x1 a. Determine the probability density function of the random variable X b. Determine the probability random variable x from ½ to 1 c. Is the probability density function a valid PDF?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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