Suppose that you specify that the range is to be all numbers between 0-4. Call the number generated y. Then the density curve of the random variable y has constant height between 0-4 and height 0 elsewhere.
a. what is the height of the density curve = 0.25
b. use your graph from a and the fact that probability is area under the curve to dfind P(Y<1.8)
c. Find P (0.6<Y<1.8)
d. Find P(Y>0.9)
Suppose that you specify that the range is to be all numbers between 0-4. Call the...
Many random number generators allow users to specify the range of the random numbers to be produced. Suppose that you specify that the random number Y can take any value between 0 and 2. Then the density curve of the outcomes has constant height between 0 and 2, and height 0 elsewhere. B) What is the height of the density curve between 0 and 2? Draw a graph of the density curve. C)Use your graph from (b) and the fact...
Many random number generators allow users to specify the range of the random numbers to be produced. Suppose that you specify that the range is to be all numbers between 0 and 5. Call the random number generated Y. Then the density curve of the random variable Y has constant height between 0 and 5, and height 0 elsewhere. (a) What is the height of the density curve between 0 and 5? (Enter your answer to two decimal places.) c)...
Many random number generators allow users to specify the range of the random numbers to be produced. Suppose that you specify that the range is to be all numbers between 0 and 5. Call the random number generated Y. Then the density curve of the random variable Y has constant height between 0 and 5, and height 0 elsewhere. 1. Use Excel to generate 100 random values from the above distribution. Construct a histogram for generated values [ Note: use...
Many random number generators allow users to specify the range of random numbers to be produced. Suppose that you specify that the random number Y can take any value between 0 and 2. Then the density curve of the outcomes has constant height between 0 and 2, and height is 0 elsewhere. P(0.5<Y<1.3) P(Y≥0.8) =
4.60 The sum of two uniform random numbers. Generate two random numbers between 0 and 1 and take Y to be their sum. Then Y is a continuous random variable that can take any value between 0 and 2. The density curve of Y is the triangle shown in Figure 4.12. (a) Verify by geometry that the area under this curve is 1. (b) What is the probability that Y is less than 1? [Sketch the density curve, shade the...
A random number generator will spread its output uniformly across the entire interval from 0 to 1 as we allow it to generate a long sequence of numbers. The results of many trials are represented by the density curve of a uniform distribution. This density curve appears in red in the given figure. It has height 1 over the interval from 0 to 1, and height 0 everywhere else. The area under the density curve is 1: the area of...
The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.85 and 0.96? (c) What is the probability of generating a number greater than 0.88? (a) Choose the correct graph of the uniform density function below. ОА. OB. OC. A Density Density A Density ON ON...
Suppose 6 numbers are generated by a computer, each uniform on the interval (0, 1). Let Y be the random variable representing the smallest of the numbers. (a) Show that the probability density of Y is given by py (t) -61-t)5, 0t <1 [51 Hint: The probability density for the r-th largest random variable can be derived using the Beta distribution by letting a = r and ?-n-r +1. (b) What is the probability that the smallest number is less...
et Yi and Y, be continuous random variables with the following joint probability density function 0, elsewhere. (a) Find E(Y1Y ) and E(YY-2) (b) Find the CDF and pdf of U mYo/Y. Your work should include a graph that supports your computatio Specify the domain where the pdf is positive.
Generate two random numbers between 0 and 1 and take X to be their sum. The sum X can take any value between 0 and 2. The density curve of X is the triangle in the figure. Height 1 0