Define the following functions, and verify if cubic
splie on given interval, also determine if natural
spline.
Define the following functions, and verify if cubic splie on given interval, also determine if natural...
Define *() = -5 + 8x - 6x + 2x on 1 <=52 and 8(1) = 27 - 40z +18r? - 22 on 2 <=3 Verify that s(2) is a cubic spline function on 1,3]. Is it a natural spline function on this interval?
Q8 Spline 15 Points Define s(2) = -5 + 8x6x2 + 2x2 on 1 < x <2, and 8(x) = 27 402 + 1822. on 2<< <3 Verify that s() is a cubic spline function on (1,3). Is it a natural spline function on this interval?
Alpha=9 beta=3 yazarsin 2. ( 20p.) Consider the cubic spline for a function f on (0,2) defined by 2x3 + x² +rx +1 if 0 <x<1 S(x) = (x - 1)3 + c(x - 1)2 + d(x - 1) + B if 1<x<2 = {(2-1) where r,c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
2. Consider the cubic spline for a function f on [0, 2] defined by S(x) = { ={ (z. 2x3 + ax2 + rx +1 if 0 < x <1 (x - 1)3 + c(x - 1)2 + d(x - 1) + ß if 1 < x < 2 where r, c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
beta is 1 2. ( 20p.) Consider the cubic spline for a function f on (0, 2) defined by 223 + ax2 + rx + 1 if 0 < x < 1 S(X) = (.x - 1)3 + c(x - 1)2 + d(x - 1) + B if i < x < 2 S(x) = { where r, c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
Define the random variable Y = -2X. Determine the cumulative distribution function (CDF) of Y . Make sure to completely specify this function. Explain. Consider a random variable X with the following probability density function (PDF): s 2+2 if –2 < x < 2, fx(x) = { 0 otherwise. This random variable X is used in parts a, b, and c of this problem.
12 Verify that the following function is a probability mass function, and determine the requested probabilities. [Give exact answers in form of fraction.] f(x)-(5/6)(1/6)" x=0,1,2, , (a) P(X= 2) (b) P(X s 2)-.uI = i (c) P(X > 2)= (d) P(X21) = T Your answer is partially correct. Try again. Verify that the following function is a probability mass function, and determine the requested probabilities f (x)3x+3 45x 0, 1, 2,3,4 Is the function a probability mass function? Give exact...
Verify that the following function is a probability mass function, and determine the requested probabilities. 4x+2 50' Is the function a probability mass function? Give exact answers in form of fraction (a) P(X 4) (b) P(X s 1)- (c) P(2 s X <4) (d) P(X> -10) Statistical Tables an
Actual lengths of stay at a hospital's emergency department in 2009 are shown in the following table (rounded to the nearest hour). Length of stay is the total of wait and service times. Some longer stays are also approximated as 15 hours in this table. Hours Count Percent 1 13 2.60 2 57 11.40 82 16.40 4 101 20.20 5 86 17.20 6 69 13.80 7 40 8.00 11 2.20 9 18 3.60 10 12 2.40 15 2.20 Determine the...
3. One period of a signal is given by the following equation: +1 1 0<t <3 x(t) = 3 NI+ 3 st 35 5 st 57 N Hint: Use the heaviside function in MATLAB to define x(t) for each time interval. Compute and plot for two periods the approximations of x(t) using 1. Complex Exponential Fourier Series computing 7 and 15 terms 2. Trigonometric Fourier Series computing 11 and 17 terms Note: You should get two figures at the end...