Let R = A sin q, where A is a fixed constant and q is uniformly...
Let R = A sin q, where A is a fixed constant and q is uniformly distributed on (pi/2, pi/2). Such a random variable R arises in the theory of ballistics. If a projectile is fired from the origin at an angle a from the earth with speed n, then the point R at which it returns to the earth can be expressed as R = (v^2/g) sin 2a, where g is the gravitational constant, equal to 980 centimeters per second squared.
(i) Find the probability density function (pdf) of R
(ii) Find cumulative distribution function (CDF) of R
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41. Find the distribution of R-A sin θ, where A is a fixed constant and θ is uniformly distributed on (-π/2, π/2). Such...
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please show worked problem;
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6. Suppose that K is a positive constant and f(x) = K sin x is a pdf on 0 < x <T. (a) Find K. (b) Find the cumulative distribution function (cdf) off. (c) Find the inverse cdf off.
4) (12pt) An unknown mass M is non-uniformly distributed along a semi-circular arc of radius R such that the linear density is given by (ф)-16 sin®. where Mo is a constant and the angle φ is measured counterclockwise with respect to the positive x-axis. (a) In terms of R and A. what is the mass of the ring? (b) Derive an expression for the gravitational force of the ring on the particle of mass m at the center of the...
please show worked problem;
The range R of a projectile fired from the origin over horizontal ground is the distance from the origin to the point of impact. If the projectile is fired with an initial velocity v0 at an angle a with the horizontal, then the range is given by the formula below, where g is the downward acceleration due to gravity. Find the angle a for which the range R is the largest possible. R = v^2/g sin...
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