You want to understand changes and In the S&P 500 and nNIKKE in a certain day are dependent. Define the random variable S&P 500 to take value 1 if the S&P 500 goes up today and -1 if the 5P 500 down. Similary , the random variable NIKKEI takes value 1 if the NIKKEI goes up today and -1 otherwise. Given P( S&P 500= 1) = 0.5 P(NiKKEI = 1 ) = 0.6 and P(S&P500 =1 | NIKKEI =1) = 0.6 calculate

(1) P(NIKKEI=1/S8P500=1);

(2) P(SRPS00=-1/NKKEI=1);

(3 ) P( S&P500 = -1 | NIKKEI = -1) ;

(4) Are S &P500 and NIKKEI independent :