Question: Question 6. A Gaussian random variable with mean 0 and variance 10 and an Exponentially distributed random variable with mean 1 fall in love

Question 6. A Gaussian random variable with mean 0 and variance 10 and an Exponentially distributed random variable with mean 1 fall in love at first chat. As they chat about meeting in person, they decide to do the following. Each one of them draws a number from their distribution independently of the other. In case both the drawn numbers have the same sign (positive or negative), they will meet in person. Else, they will not meet. Derive the probability that they will meet?

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To find the probability that they will meet we can use the concept of convolution of probability distributions The Gaussian random variable with mean ... View full answer

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