A straight line is drawn at random through a point (0, 1) (Figure 22). Find the probability density of the random variable n = 1 cos p. A(0,2) FIGURE 22
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- The probability density function of the random variable X is as in the picture with λ> 0. Find the moments estimator (λ^) of the parameter λ.What is the probability density function (PDF) of cos (2pi*t)?A point D is chosen on the line AB, whose midpointis C and whose length is a. If X, the distance from D toA, is a random variable having the uniform density withα = 0 and β = a, what is the probability that AD, BD,and AC will form a triangle?
- If X and Y are random variables and X is a geometric random variable where p = 0.1 then what is the probability mass function of Y = sin(X*pi) ?Suppose that the random variable B has the standard normal density. What is the conditional probability density function of the sum of the two roots of the quadratic equation x2 + 2Bx + 1 = 0 given that the two roots are real? KINDLY REQUEST YOU TO PROVIDE ME WITH COMPLETE SOLUTIONHere, we have a table of probability mass functions for the joint variables X and Y. Some entries of the table are left blank, please find the value for the entry marked A.
- The life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2P(x)=12e-x/2for x in [0,∞)[0,∞). Find the probability that a randomly selected laptop battery will last between 3 and 8 years?According to the figure, demonstrate the density function of the triangular distribution, taking into account that the area of the triangle is 1.Find the moment generating function MU(t) for the standard uniform random variable U (the continuous random variable whose density function is 1 on [0,1] and 0 elsewhere)
- Suppose that Y1, . . . , Yn is a random sample from a population whose density function isOn a production line, parts are produced with a certain average size, but the exact size of each part varies due to the imprecision of the production process. Suppose that the difference between the size of the pieces produced (in millimeters) and the average size, which we will call production error, can be modeled as a continuous random variable X with a probability density function given by f(x) = 2, 5e^(-5|x|), for x E R (is in the image). Parts where the production error is less than -0.46 mm or greater than 0.46 mm should be discarded. Calculate (approximating to 4 decimal places): a) What is the proportion of parts that the company discards in its production process? b) What is the proportion of parts produced where the production error is positive? c) Knowing that for a given part the production error is positive, what is the probability of this part being discarded?Based on this density, what is the probability that X is between 0.5 and 1.5? Possible answers are 1/2, 1, 1/3, 3/4. Please show steps on how answer was obtained.