The random variable X has a probability density function given by: 0S xS 1; Ske, f(x) = to. otherwise. Then k is equal to: k = The above None of these k = = k= e4-1
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- A filling station recieves its supply of gasoline once a week. Its weekly volume of sales in thousands of gallons is a random variable with probability density function f(x) = 5*(1-x)4 for 0 less than or equal to x and x less than or equal to 1 and f(x) = 0 otherwise. Find the capacity of its tank so that the probability of its supply being exhausted in a given week is 10%A continuous random variable X has the probability density function f(x) = (4-x)/8, 0 ≤ x ≤ 4. Find the expected value of XDefine random variable X ~ Uniform(0, 8). a) What is the probability density function f(X)?
- Suppose a continuous random variable X has the probability density function given below. Find the probability that X is at least .6 F(x) = {3x^2, if 0 ≤ x ≤1 0, for x otherwiseA continuous random variable has probability density function given by F(x)={kx^2 , 0<=x<=1 K(3-2x)^2 , 1<=x<=2 0,otherwise} i) Find the value of kii) Find P(1.5 <= x <= 2.5)iii) Find P(x =1.55)A fair coin and 2 weighted coins with Pr[H]= 3/4 are in a bag. One is selected at random and then flipped twice. If X is the number of heads flipped, how many distinct values of X are possible? Find the probability density function of X?
- X is a continuous random variable with probability density function of f(x) = k(6x-3x^2), 0<=x<=2 a. Show that k = 1/4 makes f(x) a valid probability density function. b. using k = 1/4, find the mean of X. c. Using k=1/4, find the cumulative distribution function F(x) of X. (Include the appropriate domain.)The random variable X has a uniform density function over the interval [-1, 1]. a. Sketch the probability density function of X. Find the mean and variance of X .The probability density function of a continuous random variable is given by y=2x−4 from x=2 to x=3. (a) Draw the graph of the density curve for the continuous random variable. (b) Verify it is a probability density function. (c) Compute P(X≤2.75).