1 Starting With Matlab 2 Creating Arrays 3 Mathematical Operations With Arrays 4 Using Script Files And Managing Data 5 Two-dimensional Plots 6 Programming In Matlab 7 User-defined Functions And Function Files 8 Polynomials, Curve Fitting, And Interpolation 9 Applications In Numerical Analysis 10 Three-dimensional Plots 11 Symbolic Math Chapter1: Starting With Matlab
Chapter Questions Section: Chapter Questions
Problem 1P Problem 2P: Calculate: (a) 8+802.6+e3.53 (b) 175)+733.131/4+550.41 Problem 3P: Calculate: (a) 23+453160.7+log10589006 (b) (36.12.25)(e2.3+20) Problem 4P: Calculate: (a) 3.822.754125+5.2+1.853.5 (b) 2.110615.21053610113 Problem 5P: Calculate: (a)sin0.2cos/6+tan72 (b) (tan64cos15)+sin237cos220 Problem 6P: Define the varialbe z as z = 4.5; than evaluate: (a) 0.44+3.1z2162.3z80.7 (b) z323/z2+17.53 Problem 7P: Define the variable t as t= 3.2; then evalute: (a) 12e2t3.81t3 (b) 6t2+6t2t21 Problem 8P: Define the variable xandy as x = 6.5 and y = 3.8; then evaluate: (a) x2+y22/3+xyyx (b) x+yxy2+2x2xy2 Problem 9P: Define the variables a, b, c, and d as: c= 4.6, d = 1.7, a = cd2, and b=c+acd; then evaluate: (a)... Problem 10P: Two trigonometric identities are given by: (a) cos2xsin2x=12sin2x (b) tanxsinx2tanx=1cosx2 For each... Problem 11P: Two trigonometric identities are given by: (a) sinx+cosx2=1+2sinxcosx (b)... Problem 12P: Define two variables: alpha =8, and beta = 6. Using these variables, show that the following... Problem 13P: Given: x2cosxdx=2xcosx+x22sinx . Use MATLAB to calculaet the following difinite integral:... Problem 14P: A rectangular box has the dimensions shown. (a) Determine the angle BAC to the nearest degree. (b)... Problem 15P: The are length of a segment of a parabola ABC is given by: LABC=a2+4h2+2ha+2ha2+1 Determine LABC if... Problem 16P: The three shown circles, with radius 15 in., 10.5 in., and 4.5 in., are tangent to each other. (a)... Problem 17P: A frustum of cone is filled with ice cream such that the portion above the cone is a hemisphere.... Problem 18P: 18. In the triangle shown a =27 in., b 43 in., c=57 in. Define a, b, and c as variables, and then:... Problem 19P: For the triangle shown, a = 72°, ß=43°, and its perimeter is p = 114 mm. Define a, ß, and p, as... Problem 20P: The distance d from a point P (xp,yp,zp) to the line that passes through the two points A (xA,yA,zA)... Problem 21P: The perimeter of an ellipse can be approximated by: P=(a+b)3(3a+b)(a+3b)a+b Calculate the perimeter... Problem 22P: A total of 4217 eggs have w be packed in boxes that can hold 36 eggs each. By typing one line... Problem 23P: A total of 777 people have to be transported using buses that have 46 seats and vans that have 12... Problem 24P: Change the display to format long g. Assign the number 7E8/13 to a variable, and then use the... Problem 25P: The voltage difference Vabbetween points a and b in the Wheatstone bride circuit is given by:... Problem 26P: The current in a series RCL circuit is given by: I=VR2(L1C)2 Where =2 f. Calculate I for the... Problem 27P: The monthly payment M of a mortgage P for n years with a fixed annual interest rate r can be... Problem 28P: The number of permutations nProf taking r Objects out of n objects without repetition is given by:... Problem 29P: The number of combinations Cn,r of taking r objects out of n objects is given by: aye In the... Problem 30P: The equivalent resistance of two resistors R1and R2connected in parallel is given by Req=R1R2R1+R2 .... Problem 31P: The output voltage Voutin the circuit shown is given by (Millman’s theorem):... Problem 32P: Radioactive decay of carbon-14 is used for estimating the age of organic material. The decay is... Problem 33P: The greatest common divisor is the largest positive integer that divides the numbers without a... Problem 34P: The amount of energy E (in joules) that is released by an earthquake is given by: E=1.741019101.44M... Problem 35P: According to the Doppler effect of light, the perceived wavelength ?p, of a light source with a... Problem 36P: Newton’s law of cooling gives the temperature T(t) of an object at time tin terms of T0, its... Problem 37P: The velocity v and the falling distance d as a function of time of a skydiver that experience the... Problem 38P: Use the Help Window to find a display format that displays the output as a ratio of integers. For... Problem 39P: Gosper’s approximation for factorials is given by: n!=2n+13nnen Use the formula for calculating 19!.... Problem 40P: According to Newton’s law of universal gravitation, the attraction force between two bodies is given... Problem 1P
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Section: Probabilty Density Functions
Transcribed Image Text: **Problem Statement:**
Let \( X \) be a random variable with probability density function (pdf) given below. Find the constant \( c \) such that this is a valid probability density function.
\[
f(x) =
\begin{cases}
cx^2 & \text{for } 0 \leq x < 1, \\
c(2-x)^2 & \text{for } 1 \leq x \leq 2, \\
0 & \text{otherwise.}
\end{cases}
\]
**Explanation:**
The function \( f(x) \) is a piecewise function defined on the interval from 0 to 2. It consists of two parts:
1. For \( 0 \leq x < 1 \), the function is \( cx^2 \).
2. For \( 1 \leq x \leq 2 \), the function is \( c(2-x)^2 \).
Outside the interval [0, 2], the function is zero.
To ensure this is a valid pdf, the integral of \( f(x) \) over its entire range must equal 1.
\[ \int_{-\infty}^{\infty} f(x) \, dx = 1 \]
This requirement translates to:
\[ \int_{0}^{1} cx^2 \, dx + \int_{1}^{2} c(2-x)^2 \, dx = 1 \]
By solving this equation, we can determine the value of \( c \).
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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![**Problem Statement:**
Let \( X \) be a random variable with probability density function (pdf) given below. Find the constant \( c \) such that this is a valid probability density function.
\[
f(x) =
\begin{cases}
cx^2 & \text{for } 0 \leq x < 1, \\
c(2-x)^2 & \text{for } 1 \leq x \leq 2, \\
0 & \text{otherwise.}
\end{cases}
\]
**Explanation:**
The function \( f(x) \) is a piecewise function defined on the interval from 0 to 2. It consists of two parts:
1. For \( 0 \leq x < 1 \), the function is \( cx^2 \).
2. For \( 1 \leq x \leq 2 \), the function is \( c(2-x)^2 \).
Outside the interval [0, 2], the function is zero.
To ensure this is a valid pdf, the integral of \( f(x) \) over its entire range must equal 1.
\[ \int_{-\infty}^{\infty} f(x) \, dx = 1 \]
This requirement translates to:
\[ \int_{0}^{1} cx^2 \, dx + \int_{1}^{2} c(2-x)^2 \, dx = 1 \]
By solving this equation, we can determine the value of \( c \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b45ec80-7eee-4c10-9c37-d097772a8db5%2Ff9985c9e-fef6-46b9-869e-93846ef93554%2Fwop7w6v_processed.png&w=3840&q=75)
