3. Suppose that Y is a continuous random variable with pdf су otherwise (a) Find the...
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
y + 155 lb. 4. (15 points) Let Y be a continuous random variable with the probability density function fy() = iSys 4 and fy() 0 otherwise. (a) Find the value of e for which fy() is a pdf. (b) Find P(Y = 3). (c) Find P(2 SY S 3). (d) Find P(2 <Y S 3). - han
k-y Suppose g (y)- K0 otherwise is a pdf for a continuous random variable Y Find P(Y s 1) (3 decimal accuracy). Number A statistician at Stats Canada wishes to test the average amount of adult smokers (19 and over) within the city of Welland. He obtained a srs of 1000 people within welland, and found that 700 people smoked, while 300 people did not smoke. Estimate the proportion of non-smokers in the population. (Your answer should be in a...
2. The actual tracking weight of a stereo cartridge that can be set to track at 3 g on a particular changer can be regarded as a continuous random variable X with pdf fx(x) otherwise a. Find the value of k so that fx is a valid pdf. b What is the probability that the actual tracking weight (X) is greater than the prescribed weight of 3 g? c. What is the probability that the actual weight is between 2.75...
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)
(22pts) 6. Suppose X is a continuous random variable with the pdf f(x) is given by $(x) = { 1 + 2 OSIS 1; Osasi otherwise. (4 pts) a Verify f(x) is a valid pdf. (4 pts) b. Find the cumulative distribution function (cdt) of X (4 pts) c. Find P(OSX30.5). (5 pts) d. Find E(X). (5 pts) e. Find V(x)
3. Suppose that Yi and 2 are continuous random variables with joint pdf given by and zero otherwise, for some constant c >。 (a) Find the value of c. (b) Are Yi and Y2 independent ? Justify your answer. (c) Let Y = Yi + ½. compute the probability P(Y 3). (d) Let U and V be independent continuous random variables having the same (marginal) distri- 3 MARKS 1 MARK 3 MARKS bution as Y2. Identify the distribution of random...
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
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)
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 <