A real number is to be selected at random from the interval [-5,
5]. There is a probability of 0.7 that the result will fall in the
range [-5, -1], and all numbers from that interval have the same
relative likelihood. Each number in the range (-1, 3) has twice the
relative likelihood as each number in the range [3, 5].
a. Plot the PDF and CDF of the random variable described by this
probability distribution.
b. Find the probability that the random variable takes on a value
between -0.5 and 0.5.
A real number is to be selected at random from the interval [-5, 5]. There is...
The rand() function generates a random real number between 0 and 1, but what if we want real numbers in a different range? Use the rand function to generate a 4x5 matrix with random real numbers between 5 and 10. Store your result in the variable "mat".
If the range of a random variable X contains an interval of real numbers, then X is a
4. Suppose a random number generator generates 20 numbers per second, where each number is drawn uniformly from the interval 9,10), independently of all other numbers. We are interested in the event that one of the drawn numbers is very close to Usain Bolt's 100m sprint world record, that is, that this number belongs to the interval (9.575, 9.585). (a) Suppose that the random number generator runs for 10 seconds. Use the Poisson approximation to estimate the probability that it...
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...
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a random variable X with the CDF given below: 2 F(x)lTe; x20 (a) Plot the CDF by hand. (b) Derive the pdf of this random variable. (c) Compute the P(Xs0.4) 0; x<0 (d) Compute the probability that a randomly selected transistor operates for at least 200 hours. Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a...
5000) of uniformly distributed random numbers between 1 Generate a large number (1000 or and 2 (HINT: use the rand command for generating a uniformly distributed random variable between 0 and 1 and then move it!). b Plot the pdf of the distribution. Use the hist command to obtain the number of samples in a random numbers, define binx as a vector with bins on the x-axis (binx = 1:0.01:2). P histx,binx) will provide you the weights pdf. Compare with...
3. Suppose a value is chosen "at random" in the interval [0,6]. In other words, r is an observed value of a random variable X U(0,6). The random variable X divides the interval [0,6] into two subintervals, the lengths of which are X and 6- X respectively. Denote by Y min(X, 6-X), the length of the shorter one of the two intervals. Find e probability PY> ) for any given y. Then find both the cdf and the pdf of...
4. Consider a continuous random variable X that is normally distributed with mean 4 and variance 10. i. Draw (as accurately as you can) the pdf of X. Carefully label axes. ii. Draw (as accurately as you can) the cdf of X. Carefully label axes. iii. At what value of x does the cdf take on the value 0.5? Label this in your diagram. iv. In the diagram of your pdf, label the area that represents the probability that X...
7. For a discrete random variable, the set of possible values is a. an interval of real numbers. b. a set of numbers that is countable. c. a set of numbers that has a finite number of numbers. d. none of the above. 8. Let X be a continuous random variable, then P( X = 0) is a. 0.00001. b. zero. c. can be large in some random variable. d. none of the above. 9. For a discrete random variable,...
Please answer the question clearly . The number of minutes that a flight from Phoenix to Tucson is late is a random variable, X with probability density (PDF) given by 21s(36-2.2), 0, _6 < x < 6 otherwise where negative values indicate the flight was early and positive values indicate the flight was late a) Find the distribution function (CDF) for X b) Find the probability that one of these flights will be at least1 nute late. 5. The distribution...