Please answer ASAP 2) Choose a point at random from the unit square [0, 1] × [0, 1]. We also choose the second random point, independent of the first, uniformly on the line segment between (0, 0) and (1, 0). The random variable A is the area of a triangle with its corners at (0, 0) and the two selected points. Find the probability density function (pdf) of A
Please answer ASAP 2) Choose a point at random from the unit square [0, 1] ×...
Can someone please answer these three questions ASAP? 1) A biased coin with probability of heads p, is tossed n times. Let X and Y be the total number of heads and tails, respectively. What is the correlation ρ(X, Y )? 2) Choose a point at random from the unit square [0, 1] × [0, 1]. We also choose the second random point, independent of the first, uniformly on the line segment between (0, 0) and (1, 0). The random...
Choose a point at random in the square with sides 0 <=x≤1 and ≤ y ≤ 1. This means that the probability that the point falls in any region within the square is the area of that region. Let X be the x coordinate and Y be the y coordinate of the point chosen. Find the conditional probability Pr(Y<1/3|Y>X). Hint Sketch the square and the events Y<1/3 and Y>X
3. A point (X, Y) is uniformly distributed on the unit square (0, 1]2. Let 0 be the angle between the r-axis and the line segment that connects (0,0) to the point (X, Y). Find the expected value El9] (Hint: recall that conin 0 and an
Choose a point at random in the square withsides 0≤x≤1and0≤y≤1. This means that the probabilitythat the point falls in any region within the square is the area ofthat region. LetXbe thexcoordinate andYbe theycoordinate ofthe point chosen. Find the conditional probability Pr(Y<1/3|Y>X).HintSketch the square and the eventsY<1/3andY>X
Suppose a point is picked at random in the unit square. If it is known that the point is in the rectangle bounded by y = 0, y = 1, x = 0, x = 1/2 , what is the probability that the point is in the triangle bounded by y = 0, x = 1/2, x + y = 1.
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2. The random variable X is uniformly distributed in the interval [4,8). Find the probability density function for random variable Y if Y 6X 12 3. Two independent random variables X and y are given with their distribution laws: 0.2 0.4 0.1 0.9 0.7 0.1 p. Find the distribution law and mode of the random variable Z-5XY 0.2
Problem 5 . This question considers uniform random points on the unit disc x2+92 〈 1 (a) A point (X, Y) is uniformly chosen in the unit disc. Find the CDF and PDF of its distance from the origin R X2 +Y2 (b) Compute the expected distance from the origin. (c) Determine the marginal PDF of X and Y (d) Are X and Y independent? (Justify your claims) e) One way to generate uniform random points on this disc is...
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QUESTION 1 1 points Save Answer A random variable is a uniform random variable between 0 and 8. The probability density is 1/8, when 0<x<8 and O elsewhere. What is the probability that the random variable has a value greater than 2? QUESTION 2 1 points Save Answer The total area under a probability density curve of a continuous random variable is QUESTION 3 1 points Save Answer X is a continuous random variable with probability density...
1. Let X be a random variable with variance ? > 0 and fx as a probability density function (pdf). The pdf is positive for all real numbers, that is fx(x) > 0. for all r ER Furthermore, the pdf fx is symmetric around zero, that is fx(x) = fx(-1), for all r ER Let y be the random variable given by Y = 4X2 +6X + with a,b,c E R. (i) For which values of a, b, and care...
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2- Choose the correct answer If the continuous random variable X is uniformly distributed with a mean of 70 and a standard deviation of (10v3). The probability that X lies between 80 and 110 is: a. Farundom variable hass pobabiliy densitE osone o the ab A 1/4 D 2/3 b. If a random variable X has a probability density functiontada 30 +4) 0sxs1 then the variance of X is closest to A/0.084 rre . B 0.519 С...