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. Let the random variable be a random number with the uniform density curve in the given figure. The probability of any event is the area under the density curve
and above the event in question. As Figure (a) illustrates, the
probability that the random number generator produces a number X
between 0.3 and 0.7 is Similarly,
Find the following: P(X ≥ 0.3) = _______ . P(X ≤ 0.3) = _______ . P(X > 0.3) = _______ . P(X < 0.3) = _______ . P(X = 0.3) = _______ .
Find the following: P(0.25 < X ≤ 0.6) = _______ . P(0.6 ≤ X < 1.3) = _______ .P(X < 0.15 or X > 0.8) = _______ . P(X < 0.3 and X > 0.7) = _______ . |
A random number generator will spread its output uniformly across the entire interval from 0 to...
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...
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...
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)
ketch the graph of the probability density function over the indicated interval. 2x 9 [0, 3] y y 0.7 0.7 0.6 0.6 0.51 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 2 3 y у 0.7 0.7 0.6 0.6 0.5 0.54 0.4 0.41 0.3 0.3 0.2 0.2 y 0.71 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 2 Find the indicated probabilities. (a) PO < x < 2) (b) P(1 < x < 2)...
Problem 2. Suppose that a uniformly distributed random number X in [0, 1] is found by calling a random number generator. Then, if the call to the RNG produces the value r for X, another random number Y is computed that is uniformly distributed on (0, x). That is, X is uniform on the interval [0, 1], and the conditional distribution for Y given X -a is uniform on the interval [0,x] a) Calculate E(Y X-0.4). b) Calculate E (X...
Suppose that a continuous random variable takes on the interval from 0 to 4 that the graph of its probability density is given the blue line of Figure 7.19 on values on the interval fr t 7.2 Suppose that a continuous random variable takes on values 0 to 4 and that the graph of its probability density is given by the blue tr to e line Figure 7.19. (a) Verify that the total area under the curve is equal to...
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...
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...
In question #1 Please answer all parts A and B. And in #2 Please answer A-C. Thank You!! Score: 0 of 1 pt 2 of 10 (4 complete) HW Score: 40%, 4 of 10 pts 7.1.13 Question Help The graph to the right is the uniform probability density function for a friend who is x minutes late. (a) Find the probability that the friend is between 15 and 20 minutes late. (b) It is 10 A.M. There is a 50%...
5. A continuous random variable X follows a uniform distribution over the interval [0, 8]. (a) Find P(X> 3). (b) Instead of following a uniform distribution, suppose that X assumes values in the interval [0, 8) according to the probability density function pictured to the right. What is h the value of h? Find P(x > 3). HINT: The area of a triangle is base x height. 2 0 0