If X and Y are independent RVs, each following N (0, 3), what is the probability that the point (X, Y) lies between the lines 3X + 4Y = 5 and 3X + 4Y = 10?
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- If we know that the firm’s profit, X, is uniformly distributed between losing 0.5million dollars to profiting 0.5 million dollars,(a) What is the average?(b) What is the P(losing 0.2 million dollar < x < profiting 0.1 million dollar)?Two archers will simultaneously shoot once at a target. Let Xi , i = 1, 2, be marksman i's horizontal error, measured in meters. If the target's position is (a, b), and marksman i's shot ends up at (x, y), then Xi = (x - a). These errors are modeled by X1 ~ N(0, 0.5) and X2 ~ N(0, 1). What is the probability that both shots will be within 1 meter of the target, in the horizontal direction?Let x and y be randomly chosen from inside the circle with r = 4. For selected numbers, x+y≥ 4 and x2+y2≤16 Find the probability that the conditions will be met?
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- A metal rod of length L and a sphere of radius R are to be joined to form a small automobile part. L and R are normally distributed with the following parameters: E(L) = 2cm, E(R) = 0.5cm, V(:) =0.1^2 cm, V(R)=0.05^2 cm^2. Assume that L and R are independent. What is the probability that the total length of a single assembly is less than 2.90 cm?Anuja is at the bottom left (0, 0) of a coordinate grid of size n ∗ m, and she can only move right and up unit distance along the edges (She cannot move towards the right and above of the point (n, m)). She chooses a path randomly and every path is equally likely. What is the probability that she passes through a point (x, y) in her path? (x>=0 and x<=n and y>=0 and y<=m)The probability of the closing of the ith relay in the circuits shown is given by p_i. Let p_1 = 0.4, p_2 = 0.1, p_3 = 0.5, p_4 = 0.7, p_5 = 0.6. If all relays function independently. what is the probability that a current flows between A and B for the respective circuit?
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