w that, area under a probability density function is equal to one.
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- 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 .This will be involving the flipping of a weighted coin. Assume that the coin is weighted so that Pr[H]=3/5 and that the coin is flipped until a head appears, or 2 consecutive tails appear. The random variable X is defined to be the total number of flips of the coin. A. How many different values are possible for the random variable X? (Answer: 2) B. Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order.Decide whether the following probability density function is a member of an exponential family: P(x,a) = a*(1– a)!-x 0 < a < 1,x = {0,1}.
- Random variable T has the following Weibull probability density function (PDF):The probability density curve of a random variable X is given in the following figure. The possible values for X range from 20 to 50.Verify that the function corresponding to the figure to the right is a valid probability density function. Then find the following probabilities: a. P(x 8) c. P(7 0 for all values of x and the total area under the density function above the x-axis is O D. (Type an integer or a decimal. Do not round.) the given function is a valid probability density function.
- If Θ ∼ Uniform(a = 0, b = 3), find the probability density function of sin(Θ).Since height is a continuous numerical variable, its probability density function is represented by the smooth curve below. What is true about the area under the curve? 140 160 180 200 height (cm) The area does not represent all possible heights, so the area under the curve and probability are both 0. O The area does not represent all possible heights, so the area above the curve is 1. O The area represents all possibile heights, so the area and probability are both 100. The area represents all possible heights, so the area under the curve and probability of all the height occurring are both 1.1. The region formed by a probability density function represented by a nonconstant linear function is _______________. a. Triangular b. Trapezoidal c. None of these d. Rectangular 2. The following is true about probability density function EXCEPT _______. a. The function is always nonnegative. b. None of these c. The probability of an individual value of random variable is zero. d. The total area under the graph is 1. 3. The region formed by the probability density function representing a continuous uniform distribution is ____________. a. Triangular b. Rectangular c. Slanted Line Segment d. Horizontal Line Segment
- Find the cumulative density function for the given probability density function. 1 f(x) = 4 for 4 ≤x≤8 F(x)=, for 4 ≤x≤ 8Balls are numbered 1 through 10 (including 1 and 10) in an urn. 3 are drawn simultaneously and at random. If X is 3 times the number of even balls drawn minus 2 times the number of odd balls drawn, how many distinct values for X are there? Find the probability density function of X?Find a value of k that will make fa probability density function on the indicated interval. f(x) = kx, [1, 4] k = (Type an integer or a simplified fraction.)
