Homework Answers
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4) (20 pts) Let X be a RV with the following PDF: fx(x) = že=fal for...
4) (20 pts) Let X be a RV with the following PDF: fx(x) = že=fal for all x. Let Y = X?. (a) Compute E[X]. (b) Find the PDF of Y, fy(y). (c) Compute E[Y].
2. LetX be a continuous RV uniformly distributed over [O . Let Y-sin(X). Find the pdf...
2. LetX be a continuous RV uniformly distributed over [O . Let Y-sin(X). Find the pdf of Y
5. Suppose X has the Rayleigh density otherwise 0, a. Find the probability density function for Y...
5. Suppose X has the Rayleigh density otherwise 0, a. Find the probability density function for Y-X using Theorem 8.1.1. b. Use the result in part (a) to find E() and V(). c. Write an expression to calculate E(Y) from the Rayleigh density using LOTUS. Would this be easier or harder to use than the above approach? of variables in one dimension). Let X be s Y(X), where g is differentiable and strictly incr 1 len the PDF of Y...
Question # A.4 (a) Given that probability density function (pdf of a random variable (RV), x is a...
Question # A.4 (a) Given that probability density function (pdf of a random variable (RV), x is as follows: Px(x)-axexp(-ax) x 20 otherwise where α is a constant. Suppose y = log(x) and y is monotonic in the given range of X. Determine: (i) pdf of y; (ii) valid range of y; and, (iii) expected value of y. Answer hint:J exp(y) (b) Given that, the pdf, namely, fx(x) of a RV, x is uniformly distributed in the range (-t/2, +...
Please show all work, will rate immediately ?? find and sketch the marginal pdf fY(y) The...
Please show all work, will rate immediately ??
find and sketch the marginal pdf fY(y)
The Joint distribution function for two rondom variables X and Y is Exy(x, y) = u(x)u(y) [l-e ax cara e acx+y)] where azo Find and sketch the marginal Pdf Fy (4)
3. [30 pts.] Let X be a Gaussian random variable N (0,0). Find the PDF, fy(y),...
3. [30 pts.] Let X be a Gaussian random variable N (0,0). Find the PDF, fy(y), of the random variable: Y = X3
Q1) A-Random variable X has the following Probability Density Function (PDF) fr(x)= 부.lel s 3. (0,...
Q1) A-Random variable X has the following Probability Density Function (PDF) fr(x)= 부.lel s 3. (0, xl>3, A1-Show that fr (x) is a valid PDF. B- X is a uniform (-1,3) random variable. Let Y be the output of a clipping circuit with the input X such that Y - 80Q) where χ>0. , B1-Find P(Y-1). B2-Find P(Y 3). B3-Derive and plot the cumulative distribution function (CDF) of the random variable Y, Fy (). B4-What is the probability density function...
4.4-2. Let X and Y have the joint pdf f(x, y) r + y, = x...
4.4-2. Let X and Y have the joint pdf f(x, y) r + y, = x + y, (a) Find the marginal pdfs fx(t) and fy (v) and show that f(x,y)关fr (x)fy(y). Thus, X and Y are dependent. (b) Compute (i) μ x, (ii) μ Y. (111) 07, and (iv) 어.
(2) Figure 4 shows the top view of a force table, which will be figure 3:...
(2) Figure 4 shows the top view of a force table, which will be figure 3: Vectors on the x-y plane. used to study two-dimensional force equilibrium in this experiment. The numbers denote an- gles measured counterclockwise from the x-axis. In a trial, two forces, FR with 2.15 N in magnitude and 45° in angle and FG with 4.30 N in magnitude and 120° in angle, are applied on the center of force table, as shown. Another force FR is...
Suppose that: (a) Let V = XY . Find the joint pdf for (X, V )....
Suppose that:
(a) Let V = XY . Find the joint pdf for (X, V ). Use it to get
the pdf for V .
(b) What is the conditional pdf for X, given V = v? What does
this say about the relationship between X and V ?
(c) Show that Z = X + Y has pdf
(Do not try to simplify it.)
4) (20 pts) Let X be a RV with the following PDF: fx(x) = že=fal for all x. Let Y = X?. (a) Compute E[X]. (b) Find the PDF of Y, fy(y). (c) Compute E[Y].
2. LetX be a continuous RV uniformly distributed over [O . Let Y-sin(X). Find the pdf of Y
5. Suppose X has the Rayleigh density otherwise 0, a. Find the probability density function for Y-X using Theorem 8.1.1. b. Use the result in part (a) to find E() and V(). c. Write an expression to calculate E(Y) from the Rayleigh density using LOTUS. Would this be easier or harder to use than the above approach? of variables in one dimension). Let X be s Y(X), where g is differentiable and strictly incr 1 len the PDF of Y...
Question # A.4 (a) Given that probability density function (pdf of a random variable (RV), x is as follows: Px(x)-axexp(-ax) x 20 otherwise where α is a constant. Suppose y = log(x) and y is monotonic in the given range of X. Determine: (i) pdf of y; (ii) valid range of y; and, (iii) expected value of y. Answer hint:J exp(y) (b) Given that, the pdf, namely, fx(x) of a RV, x is uniformly distributed in the range (-t/2, +...
Please show all work, will rate immediately ??
find and sketch the marginal pdf fY(y)
The Joint distribution function for two rondom variables X and Y is Exy(x, y) = u(x)u(y) [l-e ax cara e acx+y)] where azo Find and sketch the marginal Pdf Fy (4)
3. [30 pts.] Let X be a Gaussian random variable N (0,0). Find the PDF, fy(y), of the random variable: Y = X3
Q1) A-Random variable X has the following Probability Density Function (PDF) fr(x)= 부.lel s 3. (0, xl>3, A1-Show that fr (x) is a valid PDF. B- X is a uniform (-1,3) random variable. Let Y be the output of a clipping circuit with the input X such that Y - 80Q) where χ>0. , B1-Find P(Y-1). B2-Find P(Y 3). B3-Derive and plot the cumulative distribution function (CDF) of the random variable Y, Fy (). B4-What is the probability density function...
4.4-2. Let X and Y have the joint pdf f(x, y) r + y, = x + y, (a) Find the marginal pdfs fx(t) and fy (v) and show that f(x,y)关fr (x)fy(y). Thus, X and Y are dependent. (b) Compute (i) μ x, (ii) μ Y. (111) 07, and (iv) 어.
(2) Figure 4 shows the top view of a force table, which will be figure 3: Vectors on the x-y plane. used to study two-dimensional force equilibrium in this experiment. The numbers denote an- gles measured counterclockwise from the x-axis. In a trial, two forces, FR with 2.15 N in magnitude and 45° in angle and FG with 4.30 N in magnitude and 120° in angle, are applied on the center of force table, as shown. Another force FR is...
Suppose that:
(a) Let V = XY . Find the joint pdf for (X, V ). Use it to get
the pdf for V .
(b) What is the conditional pdf for X, given V = v? What does
this say about the relationship between X and V ?
(c) Show that Z = X + Y has pdf
(Do not try to simplify it.)
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