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Molecules of a gas in a container are moving around at different speeds. Maxwell’s speed distribution law gives the
Where M is the molar mass of the gas in kg/mol, R = 8.31J/(mol K), is the gas constant, T is the temperature in kelvins, and v is the molecule’s speed in m/s. Make a 3-D plot of P(v) as a function of i and T for
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- Determine Var(X∣Y=0).arrow_forwardLet X and Y random variables have independent Gamma distributions with X-Gamma(1, 6) and Y-Gamma(2, B). a. Find the joint probability density of Z, = X + Y, Z, = X+Y a. Find the marginal pdf of Z2.arrow_forwardFor the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. f(x)= 1/93x2 , [4,7] A) find the mean B)find the standard deviation C)Find the probability that the random variable x is within one standard deviation of the mean. (round to three decimal places as needed)arrow_forward
- Consider random variable X that is exponentially distributed with E(X) = 2. Select the probability density function for X. O f(z) = e- O f(r) = 2e-2 O F(r) = 1-e-- O F(x) = 1-e-25arrow_forwardThe probability density function of a random variable, X, is: fx(x)=(8x-x4) 0≤x≤2 Determine the first three moments of its pdf, (i) about the origin, and (ii) about its mean value.arrow_forwardThe PDF of the two independent random variables X and Y are shown in the image below. fx(x) fy(y) 1/2 1/2 -1 -2 -1 Suppose Z = X+Y. Determine the probability density value at z = 0, fz(0).arrow_forward
- 3. The storm runoff X (in cubie meters per second, ems) can be modeled by a random variable with the following probability density function (PDF): fa(x) = c (x -) for 0arrow_forwardc) Let S and T be two independent random variables with probability density functions 1 f(s)= - s > 0, e elsewhere. (e) = t > 0, e 0. elsewhere. Given X = S+ Y and Y = T. Find a joint probability distribution function of X and Y. Then determine the marginal density function of Y.arrow_forwardThe random variable X models the loss in thousands of dollars due to a fire in a commercial building. Its density function is f(x) = 0.005*(20-x) for 0 being less than or equal to x and x being less than or equal to 20 and f(x)= 0 otherwise. Given that a loss due to the fire exceeds $8000, find the probability the loss exceeds $16000.arrow_forwardThe density function of a random variable is given as fx(x) = ae bx x20. Find the characteristic function and the first two moments.arrow_forwardLet X be a random variable. P(X =x) is the probability mass function is given by X: P(X = x) 1/4 1/4 1/8 3/8 Find the value of P(X21) a. 5/7 b. 6/8 c. 7/8 d. 3/8 3.arrow_forwardcan you explain how you get P(X=x)xP(Y=y). is this the joint probability mass function?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill