and all of the values of x are equally likely to occur. The graph of a uniform distribution is shown to the right. The probability density function of a uniform distribution is shown below. Show that the probability density function of a uniform distribution satisfies the two conditions for a probability density function. y = Verify the area under the curve is equal to 1. Choose the correct explanation below. A. b-a O B. The area under the curve is the area of the rectangle. (b-a) (b-a) 2 OC. The area under the curve is sum of the maximum and minimum. a+b=0+1=1 The area under the curve is two times the mean. 2- b²a): = 1 = 1 1 b-a Show that the value of the function can never be negative. Choose the correct explanation below. OA. The numerator of the probability density function is 1, so the function must always be positive. OB. The denominator of the probability density function is always positive because a 0, therefore the function must always be positive. OC. The value of b-a is less than one, therefore the value of the function must always be greater than 1.

Assume that the machine yields the item selected 90 percent of the time, and returns nothing 10 percent of the time. Three individuals attempt to use the machine. Let X be defined as the number of individuals who obtain the item selected. How many different values are possible for the random variable X? Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order.

The probability density of a random variable X is given in the figure below. From this density, the probability that X is between 0.84 and 1.3 is:

Fifty people were asked how much they paid for the last smartphone app they purchased. These data were collected. Let the random variable X be the price paid for the app, and let f(x)=P(X=x) be the probability mass function based on the result of this survey. Answer parts a through e below. a) Write f as a set of ordered pairs. (Type an ordered pair, using integers or decimals. Use a comma to separate answers as needed. Do not include the $ symbol in your answer.) Draw the probability distribution as a histogram. Choose the correct histogram below. OA OB. OC. Q Q Q Q Q Q b) Find the cumulative probability function F Price, x $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 OD. F(x)= (Type integers or decimals) c) Find f(4). f(4) = (Type an integer or a decimal.) What does f(4) represent? O A. The probability that a randomly selected person did not pay $4 for an app OB. The probability that a randomly selected person paid $4 for an app OC. The probability that a randomly selected person paid…

Select all statements that are true for density curves. The curve is symmetric and single-peaked. The curve is on or above the horizontal axis. The proportion of data values between two numbers ?a and ?b is the area under the curve between ?a and ?b. The total area under the curve is 1. The curve satisfies the 68-95-99.7% rule.