4)
as area under a density curve is 1
therefore (1/2)*height*base =1
(1/2)*h*2=1
height =h= 1
b)P(X<1)=area of shaded region =(1/2)*1*1 =0.5
c)
P(X<0.5 ) =area of shaded region =(1/2)*0.5*0.5=0.125
4. The density curve of X is the triangle shown below: a) What is the height...
2. Suppose we toss four pennies. Let X be the total number of heads showing on ali the pennies Find the probability distribution of x. 3. Suppose we roll one four-sided die and one six-sided die. Let X be the sum of the pips showing on the two dice. Find the probability distribution for x. 4. The density curve of X is the triangle shown below: a) What is the height of the triangle. b) What is the probability that...
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...
(50 points) For the probability density function shown below (a) Determine the expected value of X (b) What is the probability that X is less than 2? (c) What is the probability that X is between 1 and 3? fx (x) 0 4
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...
On the graph of a uniformly distributed continuous random variable x, the probability density function, f(x), represents Group of answer choices the height of the function at x the area under the curve at x the probability at a given value of x the area under the curve to the right of x
***Solve without derivative and please explain all the steps in your work. Thanks. 4. Uniform Distributions. A random number generator randomly selects a number from -2 to 1. It is equally likely to select any number from this interval [-2,1]. We can view this random variable as a continuous random variable. (a) What is the constant height required to ensure that the area between the x axis and the curve is exactly one in this case (note since this is...
*** SOLVE WITHOUT DERIVATIVE, USE GRAPHING CALCULATOR FUNCTION AND SHOW STEPS 4. Uniform Distributions. A random number generator randomly selects a number from -2 to 1. It is equally likely to select any number from this interval [-2,1]. We can view this random variable as a continuous random variable. (a) What is the constant height required to ensure that the area between the x axis and the curve is exactly one in this case (note since this is a uniform...
Below is a graph of a normal distribution with mean -4 and standard deviation o 3. The shaded region represents the probability of obtaining a value from this distribution that is less than 5.5. 0.4 0.3 0.2 0.1- - 5.5 -4 Shade the corresponding region under the standard normal density curve below 0.4 ? 0.3 0.2 0.1
1. Use a standard normal table to obtain the areas under the normal curve described below. Sketch a standard normal curve and shade the area of interest. a. The area either to the left of negative 1.71 or to the right of 1.09. b. The area either to the left of 0.58 or to the right of 1.63. 2. A variable is normally distributed with mean 13 and standard deviation 4 a. Find the percentage of all possible values of...
3. The shaded region represents the Below is a graph of a normal distribution with mean 1 -1 and standard deviation probability of obtaining a value from this distribution that is between 0.5 and 3.5. Shade the corresponding region under the standard normal density curve below. x 6 ?