A continuous random variable, X, has a pdf given by f(x) = cx2 , 1 <...
A continuous random variable, X, has a pdf given by f(x) = cx2 , 1 < x < 2, zero otherwise.
(a) Find the value of c so that f(x) is a legitimate p.d.f. [Before going on, use your calculator to check your work, by checking that the total area under the curve is 1.]
(b) Use the pdf to find the probability that X is greater than 1.5.
(c) Find the mean and variance of X. Your work needs to make clear that you know whether this mean is µ or ¯x, whether this variance is σ 2 or s 2 .
(d) What proportion of values for X lie within two standard deviations of the mean?
(e) Find the CDF for X.
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A continuous random variable, X, has a pdf given by f(x) = cx2 ,
1 <...
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given...
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
(a) Let X be a continuous random variable with the cdf F(x) and pdf f(.1). Find...
(a) Let X be a continuous random variable with the cdf F(x) and pdf f(.1). Find the cdf and pdf of |X|. (b) Let Z ~ N(0,1), find the cdf and pdf of |Z| (express the cdf using ” (-), the cdf of Z; give the explicit formula for the pdf).
Suppose a random variable X has the pdf f(x) =cx2 on its support [0,3]. Find the...
Suppose a random variable X has the pdf f(x) =cx2 on its support [0,3]. Find the probability X <1 and the variance of X.
Let X be a continuous random variable with PDF f(x) = { 3x^3 0<=x<=1 0 otherwise...
Let X be a continuous random variable with PDF f(x) = { 3x^3 0<=x<=1 0 otherwise Find CDF of X FInd pdf of Y
2. A continuous random variable X has PDF SPI? 1€ (-2,2] fx() = 0 otherwise (a)...
2. A continuous random variable X has PDF SPI? 1€ (-2,2] fx() = 0 otherwise (a) Find the CDF Fx (x). (b) Suppose 2 =9(X), where gle) = { " Find the (DF, PDF of
please show work and explain for my understanding. Suppose that the continuous random variable X has pdf given by: x...
please show work and explain for my understanding.
Suppose that the continuous random variable X has pdf given by: x <1 0.16x 15 x 33 f(x)= 0.06 3<x55 [124 x>5 • Find the corresponding cdf for X: You must determine the arbitrary constants. x <1 1<x3 Ex(x)={ 3< x <5 x>5 • Use the cdf to find P(2.4 <x< 10) = • Use the cdf to determine the following percentiles: the 50th percentile (median) the 80th percentile the 90th percentile
(b) Let X be a continuous random variable with pdf given by: f(x) =c#x Find the...
(b) Let X be a continuous random variable with pdf given by: f(x) =c#x Find the constant c so that f(x) is a pdf of a random variable. C (ii) Find the distribution function F(x)P(X Sx)X (ii) Find the mean and variance of X. .Col니loa, ,iaaa4
le* 4. A random variable has a pdf f(x) = lo if x > 0 if...
le* 4. A random variable has a pdf f(x) = lo if x > 0 if xso , find the cdf, mean value and variance. Tel. :
2. A continuous random variable, x, has the following pdf. 0 otherwise Find 110 (a) the...
2. A continuous random variable, x, has the following pdf. 0 otherwise Find 110 (a) the mean, (b) the variance
1. Let X be a continuous random variable with support (0, 1) and PDF defined by...
1. Let X be a continuous random variable with support (0, 1) and PDF defined by f(x) = ( cxn 0 < x < 1 0 otherwise, for some n > 1. a) Find c in terms of n. b) Derive the CDF FX(x).
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
(a) Let X be a continuous random variable with the cdf F(x) and pdf f(.1). Find the cdf and pdf of |X|. (b) Let Z ~ N(0,1), find the cdf and pdf of |Z| (express the cdf using ” (-), the cdf of Z; give the explicit formula for the pdf).
2. A continuous random variable X has PDF SPI? 1€ (-2,2] fx() = 0 otherwise (a) Find the CDF Fx (x). (b) Suppose 2 =9(X), where gle) = { " Find the (DF, PDF of
please show work and explain for my understanding.
Suppose that the continuous random variable X has pdf given by: x <1 0.16x 15 x 33 f(x)= 0.06 3<x55 [124 x>5 • Find the corresponding cdf for X: You must determine the arbitrary constants. x <1 1<x3 Ex(x)={ 3< x <5 x>5 • Use the cdf to find P(2.4 <x< 10) = • Use the cdf to determine the following percentiles: the 50th percentile (median) the 80th percentile the 90th percentile
(b) Let X be a continuous random variable with pdf given by: f(x) =c#x Find the constant c so that f(x) is a pdf of a random variable. C (ii) Find the distribution function F(x)P(X Sx)X (ii) Find the mean and variance of X. .Col니loa, ,iaaa4
le* 4. A random variable has a pdf f(x) = lo if x > 0 if xso , find the cdf, mean value and variance. Tel. :
2. A continuous random variable, x, has the following pdf. 0 otherwise Find 110 (a) the mean, (b) the variance
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