C In Problems 17 – 20 , use a graphing calculator to graph the normal probability density function f ( x ) = 1 σ 2 π e − ( x − μ ) 2 / 2 σ 2 that has the given mean μ and standard deviation σ. 18. μ = 20, σ = 5
C In Problems 17 – 20 , use a graphing calculator to graph the normal probability density function f ( x ) = 1 σ 2 π e − ( x − μ ) 2 / 2 σ 2 that has the given mean μ and standard deviation σ. 18. μ = 20, σ = 5
Solution Summary: The author illustrates the graph of the normal probability distribution f(x)=15sqrt
Q. 6 Find 30th percentile, median and 70th percentile for the following
probability density functions:
X < 0
0s X < 1
0s X s 1.3
1.3
(i) fx(x) =
3x2
1s Xs 2 (ii) fx(x) =
%3D
%3D
2-x
1.3 < X s 2
14
otherwise
0.7
otherwise
4. "Time headway" In highway traffic flow the elapsed time between the time that one car
finishes passing a fixed point and the instant that the next car begins to pass that point
is called time headway.
Now, let X = the time headway for two randomly chosen consecutive cars on a
highway during a period of heavy traffic flow. The following probability density function
of X is suggested by traffic experts:
f(x) = 0.15*e-0.15(x-0.5) for (x ≥ 0.5 sec)
0
otherwise
a. Draw f(x) from x = 0 to x= 10 sec.
b. Find P(X ≤ 5 sec) and show it on the figure you have drawn.
c. What is E[X] and Var[X] ?
d. Find Cumulative Distribution Function of X.
6. Consider an Exponential Distribution with parameter m = 0.2
A. Write the Probability Density function f(x) for this Distribution
B. Write the Cumulative Density function F(x) for this Distribution
C. What are the Mean and Standard Deviation of this Probability Density Function
Chapter 6 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
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