Let X ∼ Unif(0, 2) and Y ∼ Bi(2, 0.5). If Z is a mixture of X and Y with equal weights, graph the cumulative distribution function of Z, and find Var(Z).
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Let X ∼ Unif(0, 2) and Y ∼ Bi(2, 0.5). If Z is a mixture of X and Y
with equal weights, graph the cumulative distribution
find Var(Z).
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- It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: x 5.00 5.25 5.75 6.75 7.00 y 8 15 13 49 71 Find the equation of the least squares line . Round a and b to three decimal places. Find the correlation coefficient r for the elevation and percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation3) A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let Xi, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.A function has a graph which passes through the point (2,3) and its graph also has the property that the normal line to each point (x,y) on the graph passes through the point (2,0). Find the function?
- It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: x 5.75 6.25 6.75 7.75 8.25 y 31 26 38 74 72 Find the value of the coefficient of determination r2. Group of answer choicesLet X-T(4) and Y~ x2 (4). The following plot depicts the cumulative distribution functions of X and Y. We don't know which is which. The horizontal lines have values 25% and 75%. We denote by q1 the x-coordinate correponding to the red point and by q2 the x-coordinate corresponding to the blue point. Which of the following statements are true? 1.00 - 0.75 0.50 - 0.25+ 0.00 - The answer is : The cdf of X corresponds to the red curve while the one of Y corresponds to the blue curve. Can you explain why? DensityLet X1,., Xn all be independent exponential distributions all with the same parameter 2. What is the distribution of the minimum of (X1,. a) what is the distribution of the smallest order statistic Y, ? b) Specify both the pdf of the distribution and describe the distribution and its parameters. ,Xn)? In other words:
- Write an absolute value function f(t) to describe an individual variance from normal body temperature where t is the individual current temperatureAn individual’s income varies with his or her age. The following table shows the median income I of males of different age groups within the United States for 2012. For each age group, let the class midpoint represent theindependent variable, x. For the class “65 years and older,” we will assume that the class midpoint is 69.5. (a) Use a graphing utility to draw a scatter diagram of thedata. Comment on the type of relation that may existbetween the two variables.(b) Use a graphing utility to find the quadratic function ofbest fit that models the relation between age and medianincome.(c) Use the function found in part (b) to determine the age atwhich an individual can expect to earn the most income.(d) Use the function found in part (b) to predict the peakincome earned.(e) With a graphing utility, graph the quadratic function ofbest fit on the scatter diagram.It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: x 5.75 6.75 7.75 8.50 9.25 y 27 16 46 62 95 What percentage of the variation in y cannot be explained by the corresponding variation in x and the least-squares line? Round your answer to the nearest tenth of a percent. 3.4% 18.4% 81.6% 9.7%
- 6. Suppose you walk a hiking trail at a speed which is uniformly distributed from 4 to 6 miles per hour. The distance of the trail is 24 miles. Find the PDF of the duration of the trip. (Note: speed = distance/time)Assume x is exponentially distributed with a mean of 4. Find: a.P(X=2) b.P(X<2) c.P(X>=2) d.P(2 < X < 4)
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