The probability density function for a continuous random variable X has the form, Find the value of c. for 1 ≤ x ≤9 f(x) = otherwise Lo O 1/2 O 3/4 O 1/4 O Do not exist
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- The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.An insurance company finds that the proportion X of itssalespeople who sell more than $25,000 worth of insurance in a given week is a random variable with the beta probability density functionf(x) = 60x^3(1 - x)^2, 0 ≤ x ≤ 1.(a) Compute E(X ) and give an interpretation of thisquantity.(b) Compute Var(X ).Determine the conditional probability distribution of Y given that X = 1. Where the jointprobability density function is given by f(x,y)=1/64xy for 0 < x < 4 and 0 < y < 4.
- A continuous random Variable X has probability Density function defined by f(x) = 5-5x; 0find the value of the constant c so that the given function is a probability density function for a random variable over the specified interval. . ƒ(x) = 1/ 6 x over [3, c].If the probability density of X is given by f(x) =kx3(1 + 2x)6 for x > 00 elsewhere where k is an appropriate constant, find the probabilitydensity of the random variable Y = 2X 1 + 2X . Identify thedistribution of Y, and thus determine the value of k.
- On 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?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?Find the moment-generating function of the continuous random variable X whose probability density is given by f(x) = 1 for 0 < x < 1 0 elsewhere and use it to find μ’1,μ’2, and σ^2.
- The probability density function of the continuous random variable X defined in the set of non-negative real numbers is given as f(x) = 2.exp(-2x). What is the expected value of X?The density function for a continuous random variable X onthe interval 1 ≤ x ≤ 4 is f(x) = 4/9 x - 1/9 x^2.(a) Use f(x) to compute Pr(3 ≤ X ≤ 4).(b) Find the corresponding cumulative distribution functionF(x).(c) Use F(x) to compute Pr(3 ≤ X ≤ 4).