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Answer:
The probability that X and Y are both positive and that their sum is less or equal to 1 0.64.
Step-by-step explanation:
It is provided that the random variables <em>X</em> and <em>Y </em>follows a standard normal distribution.
That is,
It is also provided that the variables <em>X</em> and <em>Y </em>are statistically independent of each other.
Compute the probability that X and Y are both positive and that their sum is less or equal to 1 as follows:
The mean and standard deviation of <em>X</em> + <em>Y</em> are:
The probability is:
*Use the <em>z</em>-table.
Thus, the probability that X and Y are both positive and that their sum is less or equal to 1 0.64.
