THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION

question 226

Essay

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A random variable X is normally distributed with mean of 50 and variance of 50,and a random variable Y is normally distributed with mean of 100 and variance of 200.
-Given the random variables X and Y have a correlation coefficient equal to 0.50,find the mean and variance of the random variable W = 4X+3Y.

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Definitions:

Mental Health

A person's condition with regard to their psychological and emotional well-being.

Bipolar Disorder

A mental health condition marked by extreme mood swings, including emotional highs (mania or hypomania) and lows (depression).

Anxiety

A mental health disorder characterized by feelings of worry, anxiety, or fear strong enough to interfere with one's daily activities.

Affective Disorder

A category of psychiatric disorders characterized by mood disturbances, such as depression or bipolar disorder.