![3. Let X be a continuous random variable defined on the interval 0, 4] with probability density function p(r) e(1 +4) (a) Find the value of c such that p(x) is a valid probability density function b) Find the probability that X is greater than 3 (c) If X is greater than 1, find the probability X is greater than 2 d) What is the probability that X is less than some number a, assuing 0<a<4?](http://img.homeworklib.com/questions/bd8576a0-7326-11ea-979c-8f3aa1ff010b.png?x-oss-process=image/resize,w_560)
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![[자부] 36 X73 34 36 5 36 36, iマ C.](http://img.homeworklib.com/questions/bdf86cd0-7326-11ea-8e7e-a5ddd4f3a1fd.png?x-oss-process=image/resize,w_560)
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3. Let X be a continuous random variable defined on the interval 0, 4] with probability...
Let X be a continuous random variable defined on the interval [0, 4] with probability density...
Let X be a continuous random variable defined on the interval [0, 4] with probability density function p(x) = c(1 + 4x) (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is greater than 3. (c) If X is greater than 1, find the probability X is greater than 2. (d) What is the probability that X is less than some number a, assuming 0 < a <...
4. Let X be a continuous random variable defined on the interval [1, 10 with probability...
4. Let X be a continuous random variable defined on the interval [1, 10 with probability density function r2 (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is larger than 8 or less than 2 (this should be one number! (c) Find the probability that X is larger than some value a, assuming 1 < a< 10 d) Find the probability that X is more than 3
That is a PLUS sign in the equation. Let X be a continuous random variable defined...
That is a PLUS sign in the equation. Let X be a continuous random variable defined on the interval [0, 4] with probability density function p(x) = c(1 + 4x) (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is greater than 3. (c) If X is greater than 1, find the probability X is greater than 2. (d) What is the probability that X is less than...
be a continuous random variable with probability density function 3. Let for 0 r 1 a,...
be a continuous random variable with probability density function 3. Let for 0 r 1 a, for 2 < < 4 0, elsew here 2 7 fx(x) = (a) Find a to make fx(x) an acceptable probability density function. (b) Determine the (cumulative) distribution function F(x) and draw its graph.
4. Let X be a continuous random variable with probability density 1 0< x<3 -x + k =6 f(x) elsewhere 0, Evaluate k...
4. Let X be a continuous random variable with probability density 1 0< x<3 -x + k =6 f(x) elsewhere 0, Evaluate k. a. b. Find P(1 < X< 2). c. Find E(X) d. Find e. Find ox.
4. Let X be a continuous random variable with probability density 1 0
4. Let X be a continuous random variable with probability density function: x<1 0, if if|...
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
3. Let X be a continuous random variable with probability density function ax2 + bx f(0)...
3. Let X be a continuous random variable with probability density function ax2 + bx f(0) = -{ { for 0 < x <1 otherwise 0 where a and b are constants. If E(X) = 0.75, find a, b, and Var(X). 4. Show that an exponential random variable is memoryless. That is, if X is exponential with parameter > 0, then P(X > s+t | X > s) = P(X > t) for s,t> 0 Hint: see example 5.1 in...
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f...
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution function F,(x) f()dt of X and Var(X) (c) Let A be any Borel set of R. Define P by P(A) [,f dm
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution...
is a continuous random variable with the probability density function (x) = { 4x 0 <=...
is
a continuous random variable with the probability density
function
(x) = {
4x 0 <= x <= 1/2
{ -4x + 4 1/2 <= x <= 1
What is the equation for the corresponding cumulative density
function (cdf) C(x)?
[Hint: Recall that CDF is defined as C(x) = P(X<=x).]
We were unable to transcribe this imageWe were unable to transcribe this imageProblem 2. (1 point) X is a continuous random variable with the probability density function -4x+41/2sxs1 What is...
6. Let X be a continuous random variable whose probability density function is: 0, x <0,...
6. Let X be a continuous random variable whose probability density function is: 0, x <0, x20.5 Find the median un the mode. 7. Let X be a continuous random variable whose cumulative distribution function is: F(x) = 0.1x, ja 0S$s10, Find 1) the densitv function of random variable U-12-X. 0, ja x<0, I, ja x>10.
4. Let X be a continuous random variable defined on the interval [1, 10 with probability density function r2 (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is larger than 8 or less than 2 (this should be one number! (c) Find the probability that X is larger than some value a, assuming 1 < a< 10 d) Find the probability that X is more than 3
be a continuous random variable with probability density function 3. Let for 0 r 1 a, for 2 < < 4 0, elsew here 2 7 fx(x) = (a) Find a to make fx(x) an acceptable probability density function. (b) Determine the (cumulative) distribution function F(x) and draw its graph.
4. Let X be a continuous random variable with probability density 1 0< x<3 -x + k =6 f(x) elsewhere 0, Evaluate k. a. b. Find P(1 < X< 2). c. Find E(X) d. Find e. Find ox.
4. Let X be a continuous random variable with probability density 1 0
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
3. Let X be a continuous random variable with probability density function ax2 + bx f(0) = -{ { for 0 < x <1 otherwise 0 where a and b are constants. If E(X) = 0.75, find a, b, and Var(X). 4. Show that an exponential random variable is memoryless. That is, if X is exponential with parameter > 0, then P(X > s+t | X > s) = P(X > t) for s,t> 0 Hint: see example 5.1 in...
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution function F,(x) f()dt of X and Var(X) (c) Let A be any Borel set of R. Define P by P(A) [,f dm
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution...
is
a continuous random variable with the probability density
function
(x) = {
4x 0 <= x <= 1/2
{ -4x + 4 1/2 <= x <= 1
What is the equation for the corresponding cumulative density
function (cdf) C(x)?
[Hint: Recall that CDF is defined as C(x) = P(X<=x).]
We were unable to transcribe this imageWe were unable to transcribe this imageProblem 2. (1 point) X is a continuous random variable with the probability density function -4x+41/2sxs1 What is...
6. Let X be a continuous random variable whose probability density function is: 0, x <0, x20.5 Find the median un the mode. 7. Let X be a continuous random variable whose cumulative distribution function is: F(x) = 0.1x, ja 0S$s10, Find 1) the densitv function of random variable U-12-X. 0, ja x<0, I, ja x>10.
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