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) =
Given that the density curve of the outcomes has a constant height between 0 and 2, and height is 0 elsewhere. Thus the pdf of Y is:
Thus we can find probabilities.
Many random number generators allow users to specify the range of random numbers to be produced....
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...
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)
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...
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...
Let X be a random number between 0 and 1 produced by the idealized uniform random number generator. Use the density curve for X, shown below, to find the probabilities: 1 0.8+ 0.6 0.4+ 0.2 + 0.4 + 0 0.2 0.6 0.8 (a) P(0.1 X 0.8) = (b) P(X 0.8)
Let the random variable X be a random number with the uniform density curve in the figure below. Area = 0.4 Area = 0.5 Area = 0.2 Height = 1 0.3 0.7 0.5 0.8 P(X<0.5 or X > 0.8) P(0.3<X<0.7) (a) (b) Find the following probabilities. P(X 2 0.35) (a) (b) P(X = 0.35) P(0.35 < X < 1.25) (c) P(0.10 < X < 0.20 or 0.6 < X < 0.9) (d) X is not in the interval 0.5 to...
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
In this problem you'll get to use one of Java's random number generators, java.util.Random (see the docs for Random). This class generates a random double precision number uniformly distributed in the range [0.0 ... 1.0). That is, the numbers go from 0 to 1, including 0 but excluding 1. It is a common need in Java programming to generate a random integer number that's uniformly distributed in the range of [0 ... n), such as we saw in the dice...