1. Graph the probability function f(x)=kx (x = 1,2,3, 4,5; k suitable) and the distribution function....

  

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1. Graph the probability function f(x)=kx (x = 1,2,3, 4,5; k suitable) and the distribution function. 2. Graph the density function f(x) = kr (0 x 5; k suitable) and the distribution function. 3. Uniform distribution. Graph fand F when the density of X is f(x) = k = const if -2x2 and 0 else- where. Find P(0 X 2). 4. In Prob. 3 find c and such that P(-c < x < c) = 95% and P(0 < x < 7) = 95%. 5. Graph and F when f(-2) = f(2) = f(1) = f(1) =. Can f have further positive values? 6. A box contains 4 right-handed and 6 left-handed screws. Two screws are drawn at random without replacement. Let X be the number of left-handed screws drawn. Find the probabilities P(X = 0), P(X = 1). P(X 2). P(1 0, F(x) = 0 if x 0, and the density f(x). Find x such that F(x)=0.9. 9. Let X [millimeters] be the thickness of washers. Assume that X has the density f(x)=kx if 0.9x1.1 and 0 otherwise. Find k. What is the probability that a washer will have thickness between 0.95 mm and 1.05 mm? 1. Graph the probability function f(x)=kx (x = 1,2,3, 4,5; k suitable) and the distribution function. 2. Graph the density function f(x) = kr (0 x 5; k suitable) and the distribution function. 3. Uniform distribution. Graph fand F when the density of X is f(x) = k = const if -2x2 and 0 else- where. Find P(0 X 2). 4. In Prob. 3 find c and such that P(-c < x < c) = 95% and P(0 < x < 7) = 95%. 5. Graph and F when f(-2) = f(2) = f(1) = f(1) =. Can f have further positive values? 6. A box contains 4 right-handed and 6 left-handed screws. Two screws are drawn at random without replacement. Let X be the number of left-handed screws drawn. Find the probabilities P(X = 0), P(X = 1). P(X 2). P(1 0, F(x) = 0 if x 0, and the density f(x). Find x such that F(x)=0.9. 9. Let X [millimeters] be the thickness of washers. Assume that X has the density f(x)=kx if 0.9x1.1 and 0 otherwise. Find k. What is the probability that a washer will have thickness between 0.95 mm and 1.05 mm?