c) In a certain Poisson distribution the probability of 3 successes is exactly equal to the probability of 4 successes. Find its mean and standard deviation. Also find the probability of more than 1 success for the given distribution.
To solve this, we need to use the Poisson distribution formula for probability: \[ P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!} \] Where: - \( \lambda \) is the mean (also the rate of success). - \( P(X = k) \) is the probability of exactly \( k \) successes. We are given that the probability of 3 successes is equal to the probability _____ ________ ___ _______ ____ _______ ________ ___ ____ _____ _________ __________.
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b) Verify Euler’s theorem for the function
a) Integrate
a) Find the radius of the sphere which passes through the points ),1,0,0( ),,0,0,1( )0,1,0( and ).1,0
b) Solve the differential equation cos
a) It is known that 10 men out of every 100 men and 30 women out of every 1000 women are color blind. In a community, half the population is male. Using Baye’s theorem find the probability that a color blind person chosen at random from among all color blind persons in the community is male.
b) Find the term independent of a in the binomial expansion of
c) Fit a straight line for regression of Y on X from the following table.
| x | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| y | 2 | 1 | 3 | 2 | 4 | 3 | 5 |
Find the value of y when