The reaction time (in seconds) to a certain stimulus is a continuous random variable with pdf...
2. Suppose that the continuous random variable X has the pdf f(x) = cx3:0 < x < 2 (a) Find the value of the constant c so that this is a valid pdf. (10 pts) (b) Find P(X -1.5) (5 pts) (c) Find the edf of X use the c that you found in (a). (Hint: it should include three parts: x x < 2, and:2 2) (20 pts) 0,0 <
Damon's reaction time to a stimulus is 0.613 seconds. Reaction time is a ___ variable. answer- a. discrete b. continuous c. discontinuous d. nominal
7. Let X be a continuous random variable with a known pdf of f(x) = led for x>0 and being a constant. If the mean value of X is 1/3, then find the median value of X. Give your answer as a decimal rounded to four places (i.e. X.XXXX). Hint: Hmm...this looks familiar...see (6).
3. Consider a continuous random variable X with pdf given by 0, otherwise This is called the exponential distribution with parameter X. (a) Sketch the pdf and show that this is a true pdf by verifying that it integrates to 1 (b) Find P(X < 1) for λ (c) Find P(X > 1.7) for λ : 1
Additional Problem 3. If X is a continuous random variable having cdf F, then its median is defined as that value of m for which F(m) = 0.5. Find the median for random variables with the following density functions (a) f(r)-e*, x > 0 (c) f(x) 6r(1-x), 1. Additional Problem 6. Let X be a continuous random variable with pdf (a) Compute E(X), the mean of X (b) Compute Var(X), the variance of X. (c) Find an expression for Fx(r),...
o. Consider a random variable X with pdf given by fx(z) = 0 elsewhere. elsewhere. 0 (a) What is c? Plot the pdf (b) Plot the edf of X. (c) Find P(X 0.5<0.3).
3.17 A PDF for a continuous random varaiable X is defined by C 0<x<2 2C4<< 6 fx(x) = 3 C 7<<<9 0 otherwise where C is a constant. (a) Find the numerical value of C. (b) Compute Pr[1 < X < 8). (c) Find the value of M for which "fx(s)de = [fx (a)dr = 1 J-00 Mis known as the median of the random variable.
2. Let X be a continuous random variable with pdf f(x) = { cr", [w] <1, f() = 0. Otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(2) of X. (c) Use F(2) (from b) to determine P(X > 1/2). (d) Find E(X) and V(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)
14. The lifetime (in hours) of a certain piece of equipment is a continuous random variable X having range 0 x0 and density function xe s(x)-100 0, otherwise (a) Show that this is a density function (b) Compute the probability that the lifetime exceeds 20 hours, Prix> 20.