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. 17. μ = 0, σ = 1
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. 17. μ = 0, σ = 1
Solution Summary: The author illustrates the graph of the normal probability distribution with f(x)=1sigma.
Suppose that the random variable X has the probability density function
f(x) = {"
c(1- x2)
for - 1s x s1
elsewhere
What is the variance of X
A
1/2
B
1/3
1/5
D
1/4
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.
3. (a) A random variable, X, has the following probability density function:
for 0 S <2
S (m) = { (20 - 4æ)/30 for 2 S6
0.
otherwise.
1 Sketch the graph of f(2). (The sketch can be drawn on ordinary paper- no
graph paper needed.)
II. Derive the cumulative distribution function of X.
iil. Find the mean and the standard deviation of X.
Chapter 6 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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